2022 Roadmap on integrated quantum photonics

¹ University of California Santa Barbara, Santa Barbara, CA 93106, United States of America

² George Washington University, Washington, DC, United States of America

Integrated photonics is at the heart of many classical technologies, from optical communications to biosensors, LIDAR, and data center fiber interconnects. There is strong evidence that these integrated technologies will play a key role in quantum systems as they grow from few-qubit prototypes to tens of thousands of qubits [1]. The underlying laser and optical quantum technologies, with the required functionality and performance, can only be realized through the integration of these components onto quantum photonic integrated circuits (QPICs) with accompanying electronics. In the last decade, remarkable advances in quantum photonic integration and a dramatic reduction in optical losses [2] have enabled benchtop experiments to be scaled down to prototype chips with improvements in efficiency, robustness, and key performance metrics [3, 4]. The reduction in size, weight, power, and improvement in stability that will be enabled by QPICs will play a key role in increasing the degree of complexity and scale in quantum demonstrations. As an example, the timeline in figure 1 illustrates this rapid progression from few-component circuits enabling two-photon quantum interference in 2008 [5] to a decade later with devices combining more than 650 components capable of arbitrary and programmable two-qubit operations [6], enabling advances in foundational quantum mechanics, computing, communications, and metrology [7]. Today, experiments that until recently occupied an optical table, such as Boson sampling [8], diamond color-center emitter arrays [9], and multi-ion quantum logic [10, 11], have moved onchip. Despite these early advancements, the level of QPIC complexity lags that of conventional PICs, which today comprise ∼5 × 10³ components on chip. Interestingly, this progression mirrors the development of digital electronics that occurred through the 1960s and 1970s, leading to potential quantum integration scaling laws and roadmaps. Today's state-of-the-art integration, with current materials, fabrication, and packaging technologies, gives a snapshot of on-chip complexity currently achievable.

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In this roadmap article, we highlight the status, current and future challenges, and emerging technologies in several key research areas in integrated quantum photonics (figure 2), which serves as a complementary resource to the recent OIDA Roadmap on Quantum Photonics [12]. With advances in materials, PIC-based platforms, devices and circuits, fabrication and integration processes, packaging, and testing and benchmarking, we can expect a transition from single- and few-function prototypes to large-scale integration of multi-functional and reconfigurable QPICs. These circuits will play a key role in how quantum information is processed, stored, transmitted, and utilized for quantum computing, communications, metrology, and sensing. This roadmap highlights the current progress in the field of integrated quantum photonics, future challenges, and advances in science and technology needed to meet these challenges. Key areas of research and technology addressed include:

• (a)  
  PIC platforms: While silicon-based photonics has been the workhorse for QPICs owing to the low waveguide loss and the existing foundry infrastructure, other material platforms have been developed to further extend the capabilities beyond what silicon can offer [13], including III–V semiconductors, lithium niobate (LN), silicon carbide (SiC), nitrides, diamond, and tantalum pentoxide (Ta₂O₅). Future advances in quantum photonics will likely require a heterogeneous approach [14] that combines multiple PIC materials to achieve high-level functionality with integrated lasers and amplifiers, passive components, modulators, quantum frequency converters, efficient detectors or chip-to-fiber couplers, and control logic.
• (b)  
  Quantum and classical light sources and qubits: Quantum light sources generating single photons, entangled-photon pairs, squeezed light, and other non-classical states are fundamental resources for quantum information science. Quantum sources typically fall into two categories: Quantum emitters that can produce photons on-demand, and sources based on χ⁽²⁾ or χ⁽³⁾ nonlinear optics that produce photons probabilistically. Rapid progress with quantum emitters based on InAs quantum dots (QDs), defects in diamond and SiC, emissive centers in silicon, and probabilistic sources in several nonlinear PICs have already been used successfully for numerous applications in communications, computing, and networking. Further technological developments that improve PIC integration must follow to increase the photon generation quality, efficiency, and rates. Likewise, as these sources currently rely on off-chip optical pumping, improvement in their efficiency will facilitate the integration of precision and tunable pump lasers, filters, and control electronics on chip for packaged, turn-key systems. Such heterogeneous integration may demand co-design approaches beyond current single platform design rules.
• (c)  
  Quantum frequency conversion: Quantum frequency conversion (QFC) is essential to establish interconnections between quantum systems operating in different wavelength regimes, for example, to connect a trapped ion quantum processor to a neutral atom ensemble quantum memory or to an optical network featuring microwave-frequency superconducting qubits. Numerous approaches to frequency conversion exist, including optomechanics and nonlinear photonics and optoelectronics, providing exciting prospects for achieving high conversion efficiency spanning ultraviolet to telecommunications wavelengths with low added noise.
• (d)  
  Integrated detectors: To take full advantage of the low loss and high throughput afforded by integrated photonics, effective schemes for on-chip coupling of high-performance photodetectors with single- and photon-number resolving capabilities are required. Detectors based on superconducting nanowires, which operate at cryogenic temperatures, are the most promising technology to date with near-unity quantum efficiency, low jitter, and low dark count rates. However, the required cooling apparatus sets system limitations, and room-temperature approaches defeating k_BT noise would be a game-changer for QPICs. Single-photon avalanche photodiodes (APDs) are appealing due to their near-room-temperature operation, but improvements in their performance are required to compete with superconducting detectors. Notably, both technologies can be integrated with various PIC platforms through direct growth, thin film deposition, or chip-to-chip bonding.
• (e)  
  Applications: The potential impact of quantum photonic technologies is vast, ranging from all-optical quantum computing, quantum encryption, and networking to machine learning, sensing, and interfacing with other quantum systems, such as chip-scale ion traps. The key challenges are scaling up the number of integrated components, improving on-chip functionality and performance, and maintaining low excessive noise and loss, while enabling seamless assembly and packaging.

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In addition to the technological advances, transitioning from proof-of-principle prototypes to packaged and deployable systems used in quantum experiments and applications will require the investment in, and development of, a sustainable quantum photonic ecosystem that brings together interdisciplinary researchers, scientists and engineers, infrastructure and testbeds, and federal, academic, and private partnerships. Key long-term goals of this infrastructure should be to broaden access to quantum integrated technologies and to cultivate future generations of a quantum workforce through training, professional development, and mentorship. Other aspects important to the long-term ecosystem include modernized teaching labs and activities that enable hands-on approaches toquantum mechanics and photonics education. Each article in this roadmap provides an overview of a specific area, highlighting the status, current and future challenges, and advances in the science and technology to meet these challenges, together covering the plurality of fields in this exciting space.

Paul W Juodawlkis, William Loh and Cheryl Sorace-Agaskar

Status

Integrated photonic technologies will play a central role in advancing the frontiers of quantum information science and in the full realization of quantum processing, sensing, and communication applications. The required scaling (i.e. thousands to millions of quantum processing or sensing elements) and functional complexity of these quantum systems will only be possible through the high density, enhanced performance, and environmental stability afforded by photonic integrated circuits (PICs). Photonic functions that will be needed include light generation (both uncorrelated photon beams and entangled-photons), amplification, modulation, switching, routing and qubit input/output (I/O) interfacing, passive splitting/combining, filtering, frequency translation, and detection (both single photon and linear). Due to the distinct material properties required to realize these functions over the operating wavelengths (i.e. ultraviolet to near-infrared) associated with the various quantum modalities, it is highly unlikely that the required PICs can be made using a homogeneous material platform such as silicon or a single compound-semiconductor material system. Therefore, advances in quantum information science and engineering will require the development of heterogeneous material PICs that are made available to the community through a collaborative ecosystem of design, fabrication, packaging and evaluation resources.

Figure 3 depicts a generic heterogeneous PIC platform that combines the fabrication process control and yield of advanced silicon foundry toolsets with the wide-ranging materials options and flexibility of post-silicon-fab hybrid integration of materials and components. The base platform is comprised of multi-layer dielectric (i.e. silicon nitride (SiN), alumina oxide (Al₂O₃)) and silicon waveguides that are used to implement passive (e.g. figure 3(a) where a subset of layers were used [15]) and active components, and to create optimized interfaces for heterogeneous integration. Low optical losses have been achieved in both medium-confinement waveguides (<0.2 dB cm⁻¹ in SiN from 600–1650 nm, 3 dB cm⁻¹ in Al₂O₃ at 370 nm [16]) and low-confinement waveguides (0.001 dB cm⁻¹ in SiN from 1300–1650 nm). Optical sources and other non-silicon-based active devices can be added through a combination of material growth and deposition, layer transfer, wafer bonding, and pick-and-place techniques. Exemplar demonstrations of such a heterogeneous PIC platform include high-power (>300 mW) low-noise lasers incorporating flip-chipped semiconductor optical amplifiers (figure 3(d)) [17], surface-bonded optical gain media (figure 3(c)) [18, 19], and low-loss surface-bonded thin-film lithium-niobate (TFLN) waveguides (figure 3(b)) [20]. While this initial work along with the work of other photonic developers are important first steps, a more significant and coordinated effort is required to develop the platforms needed by the community.

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Current and future challenges

Advances in science and technology to meet challenges

Concluding remarks

Acknowledgments

QET Labs, University of Bristol, Bristol, United Kingdom

Silicon photonics has been pivotal for increasing the complexity and component-number of on-chip quantum circuitry and revealing the disruptive potential an engineered integrated approach can take for a quantum technology [7]. Optical circuits in silicon benefit from compatibility with established CMOS processes, and silicon's high component density, operation at telecom wavelengths, and nonlinear properties mean it ticks a lot of boxes on the wish list for an integrated photonics platform. Research also benefits from the maturity of the platform that has to date been largely developed for classical telecommunications. As a result, it has been the material of choice for many early demonstrations of building blocks for photonic quantum computing and has seen rapid growth in the number of generated photons and integrated components over the last 10 years [7, 24, 25].

Yet while silicon as a largely homogenous platform for quantum photonics provides a straightforward route to manufacturability, relying on a single material to deliver almost all of the core functions required for quantum information processing (QIP) incurs severe overheads. In silicon, or indeed in other homogenous integrated quantum photonics platforms, photon generation is spontaneous and there is no direct photon–photon interaction. The lack of deterministic methods to generate, store, and entangle photons is addressed by deploying large amounts of probabilistic measurement and feed-forward operations. The feasibility of these schemes to deliver fault tolerant quantum computing is as yet unproven.

Taking a step back, we can consider the hardware elements of a more sophisticated and intrinsically scalable photonic quantum processor. Ideally, this would comprise deterministic sources of single-photons or photonic entangled states, frequency conversion modules, quantum memories, and controlled light–matter interaction. To support the integration of some, or even all of these capabilities, a heterogeneous platform would benefit from an interfacing material with a broad transparency, such as SiN, LN, or AlN, to name a few. However, manufacturing such a heterogenous device is also extremely challenging.

Here we discuss the challenges to further scale silicon quantum photonics as a contemporary manufacturable solution for QIP. We then discuss the necessary long-term endeavour, to mass-integrate arrays of functional quantum components, as well as classical readout and control, into a heterogeneous platform for quantum computing.

To maintain its role as a contemporary option for QIP, silicon quantum photonics must continue to make progress against a number of key challenges:

Photon loss

Detectors and cryogenic operation

Switching

Interfacing photonics and electronics

The ability to drive and process electrical signals to manipulate and to measure light on a chip motivates better integration of electronics and photonics. Recent work on high-bandwidth detection of squeezed light using a silicon photonic integrated chip wire-bonded directly to a silicon electronics die demonstrated the importance of leveraging the best performing photonic and electronics components, even if they are not available from the same foundry process [33] (figure 4). By bringing the components close together, the total device capacitance in [33] was curtailed, thus enabling the highest bandwidth of shot-noise limited detector performance yet reported—a tangible advantage to a quantum application brought about by miniaturization and integration. Research into the performance of monolithic electronic–photonic integrated circuits is currently hampered by limited availability of high-performance components across both at commercial foundries and a reduced pool of simultaneous expertise in integrated photonics, high speed, low noise microelectronics and quantum technology.

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As quantum processors increase in size and complexity, chip-to-chip connectivity will become critical, not just for exploiting superior component performance in different materials, but also for devices to expand beyond a single wafer. Transmission of quantum information between silicon chips has been demonstrated using optical fibre and sophisticated locking mechanisms for stability [34]. Like approaches for powerful modern computer processors, integrated optical and electronic interposers would provide a more stable, manufacturable and scalable method of quantum and classical communication between different dies.

A grand ambition for photonic quantum technologies is to bring forth a CMOS-like manufacturable approach for heterogeneous integrated quantum photonic processors. This would enable the promised generations of disruptive quantum technologies, including fault tolerant quantum computing. Some immediate and important advancements required to achieve this can be specified.

Interfacing integrated photonics and functional components

Control and readout

Characterisation

We expect that silicon photonics will remain an important testbed for further scaling of QIP, if the key challenges can be overcome. However, the advances required to deliver a CMOS-like infrastructure for heterogeneous integrated quantum photonics, and delivery of fault tolerant quantum computing, will require significant and coordinated effort across the photonics community.

The authors thank Lawrence Rosenfeld, Jacob Bulmer, and Patrick Yard for useful discussions and suggestions. J C F M acknowledges support from European Research Council starting Grant ERC-2018-STG 803665. Support from the Engineering and Physical Sciences Research Council (EPSRC) Hub in Quantum Computing and Simulation (EP/T001062/1) is acknowledged. Fellowship support from EPSRC is acknowledged by A L (EP/N003470/1).

National Institute of Standards and Technology, United States of America

Heterogeneous integration encompasses bonding of two dissimilar materials followed by device fabrication in a single process flow. The approach has been applied in the fabrication of optoelectronic [35] and nonlinear photonic [36] devices on silicon substrates and on-chip waveguides, with gain, absorption and enhanced optical nonlinearities provided by III–V semiconductor materials. While much of the initial work involved bonding at the chip scale, bonding at the wafer scale was later also demonstrated [37]. Heterogeneous integration at the chip scale was used by Bakir et al [38] to produce, for the first time, optically pumped lasers based on III–V epitaxial QDs on a silicon substrate. Further progress led to demonstration of electrically injected QD lasers on silicon [39]. In 2017, the approach was used at the chip scale to produce SiN-based photonic circuits with integrated single-photon sources (SPSs) based on single InAs QDs [40], shown in figures 5(a)–(d). Whereas devices in this work contained multiple, randomly positioned QDs, deterministic fabrication of SPSs with QDs precisely located within GaAs nanowaveguides were demonstrated in 2019 by Schnauber et al [41], shown in figures 5(e) and (f). This later work also showed triggered and post-selected indistinguishable single-photon emission into SiN waveguides, with reported coherence lengths comparable to those obtained from InAs self-assembled QDs in GaAs-only devices, under similar optical pumping conditions. The introduction of single QDs in quantum silicon photonic circuits has the potential to greatly scale integrated quantum photonic information systems that rely on probabilistic gates, which generally require highly efficient single-photon qubit generation, low-loss waveguide interferometric networks, and highly efficient single-photon detection. On-chip single QDs may act as triggered, high-rate sources of indistinguishable photons, and can couple with high efficiency to the silicon photonic circuit through carefully designed GaAs nanophotonic structures. Single QDs strongly coupled to on-chip cavities furthermore offer a path towards single-photon nonlinearities, which could enable deterministic quantum gates on chip [42]. It is worth noting that hybrid integration techniques, in which III–V and silicon-based devices are produced in separate runs and then brought together through methods such as pick-and-place or transfer-printing, have also successfully produced silicon photonic devices with on-chip QD SPSs [4].

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Deterministic fabrication of on-chip devices with functionality based on single epitaxial QDs currently poses a formidable challenge towards scalable integration. Single-dot device functionality requires the creation of an efficient interface between a single QD and a single, efficiently accessible, spatially confined optical mode—e.g. a cavity resonance or waveguide mode. This in turn requires positioning the single dot with sub-wavelength-scale precision at specific locations within the extent of the spatial optical mode, in order to maximize coupling. While site-selective QD growth techniques have allowed such an achievement [43], self-assembled QDs produced via the Stranski–Krastanow (S–K) growth mode have generally demonstrated superior coherence, a critical characteristic for quantum photonic applications. In contrast with site-controlled dots, self-assembled QDs are produced at random positions across the growth wafer surface, and generally present a wide heterogeneity of optical properties such as transition energies, quantum yield and coherence times. Deterministic fabrication of a single S–K dot device, then, requires first that an individual emitter with the desirable optical properties be identified within largely heterogeneous, as-grown ensemble. Subsequently, the photonic geometry that supports the desired, interfacing optical mode must be fabricated around the identified QD. It is worth noting that such challenges exist for any device that derive their functionality from single quantum emitters, in both homogeneous and heterogeneous material platforms, and in hybrid and heterogenous fabrication approaches.

Advances in site-selective growth to allow better control of QD spectral homogeneity and coherence properties would significantly improve integration scalability, by allowing deterministic single QD device fabrication through standard, scalable top-down processing techniques. In the absence of such possibility, scalable integration of single S–K QD devices would greatly benefit from the development of high-throughput single-QD localization and spectroscopy systems. Ideally, such a system would allow fast identification of large number of dots emitting indistinguishable single-photons at desired wavelengths, for integration with nanophotonic geometries. Because S–K QDs occur at random locations, however, such an approach would result in randomly located single-dot devices. These devices would then have to be connected to the photonic circuit through ad hoc routes, which cannot be produced predictably with optical projection lithography. Hybrid integration techniques can in principle circumvent such issues, since prefabricated QD devices (even if produced at random locations on the origin chip) can be deterministically placed onto pre-determined locations on the destination chip. Scalable integration would, however, require high throughput device transfer techniques, which may be challenging depending particularly on alignment tolerances.

In summary, heterogeneous integration has considerable potential for large-scale quantum silicon photonic circuits with functionality based on single III–V semiconductor QDs. Although the approach in principle allows completely top-down processing, integration scalability is principally hampered by the necessity to locate and analyse QDs at an individual level prior to fabrication. Importantly, though, such non-trivial and time-consuming tasks are generally necessary in any integration platform for devices that employ single quantum emitters.

Department of Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, CA 93106, United States of America

A primary goal in quantum photonics is the construction of fully integrated and versatile quantum photonic circuits comprising tunable classical and quantum light sources, active and passive components, programmable networks, and detectors [7, 36]. Over the last decade, remarkable progress along this direction has been achieved on the silicon-on-insulator (SOI) platform, which leverages the mature manufacturing infrastructure of the semiconductor industry for high volume and low-cost production. To further extend the capabilities beyond what silicon can offer, a variety of material candidates, such as SiN, LN, and III–V semiconductors have been developed and investigated. Among the diverse photonic platforms, (aluminium) gallium arsenide [(Al)GaAs] on insulator has attracted significant interest recently [44, 45] due to its direct bandgap structure for light generation, large bandgap minimizing TPA at telecom wavelengths, and large χ⁽²⁾ and χ⁽³⁾ optical nonlinear coefficients, which are orders of magnitude higher than commonly used dielectric photonic media.

Traditionally, III–V photonic platforms suffered from high waveguide loss and low optical confinement because all of the devices were processed on a native III–V substrate [46]. (Al)GaAs-on-insulator [(Al)GaAsOI] overcomes this constraint by heterogeneously integrating an (Al)GaAs film with an oxidized Si substrate by wafer bonding technology (figure 6(a)). The high index contrast attained by this approach brings a plethora of new opportunities in nonlinear and quantum applications by enhancing the light intensity and tailoring the waveguide geometry. Another key advance for this platform is the significant reduction in waveguide loss. By combining optimized lithography, etching, and passivation, the propagation loss of AlGaAsOI waveguides (<0.2 dB cm⁻¹) is one order of magnitude lower compared to those of previous III–V platforms, which enables optical resonators with a quality factor Q beyond 3 million (figure 6(b)) [47], on par with many state-of-the-art dielectric material platforms.

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Presently, various types of nonlinear devices have been demonstrated on (Al)GaAsOI (figures 6(c)–(f)). Based on the novel direct-phase-matching between TE and TM modes, a record-high normalized second harmonic generation (SHG) efficiency >40 000% W⁻¹cm⁻² has been attained in a GaAsOI waveguide (figure 6(d)) [48]. For χ⁽³⁾-based nonlinear processes, a record-low threshold around 20 µW for Kerr comb generation is achieved in a high-Q AlGaAsOI resonator (figure 6(e)) [47], where the AlGaAs material bandgap is engineered to avoid two photon absorption at the telecom band. Similar types of waveguides are also used for efficient wavelength conversion in optical signal processing (figure 6(f)) [49] with pump power compatible with integrated laser sources.

Such high-efficiency nonlinear processes are essential for multiple quantum purposes. A recent milestone with AlGaAsOI quantum photonics is the demonstration of entangled photon pair generation from a microresonator through SFWM [50]. Combining the high Q-factor and the strong Kerr coefficient, a waveguide-integrated source exhibits a pair-generation rate greater than 20 × 10⁹ pairs s⁻¹ mW⁻² near 1550 nm, with a heralded single photon purity >99%, entanglement visibility >97% and coincidence-to-accidental ratio (CAR) >4300. The brightness of this source (2 × 10¹¹ pair s⁻¹mW⁻² GHz⁻¹ bandwidth) is about 1000-fold higher compared to traditional on-chip entangled-pair sources. Such high-efficiency and high-quality quantum light sources in AlGaAsOI points towards exciting prospects for combining state-of-the-art nonlinear components into the quantum regime and can potentially benefit a wide range of system-level applications.

Due to its short history, (Al)GaAsOI requires significant research and development in order to reach a similar level of integration as current quantum photonic circuits on silicon. Compared to the rich library of PDKs based on SOI waveguides, so far very few devices using (Al)GaAsOI have been developed to realize the necessary components in PICs, such as wavelength demultiplexing, Mach–Zehnder interferometers, modulators, and detectors. One challenge that must be overcome to support the growth of (Al)GaAsOI technology is to transition from research development level fabrication to commercial vendors and/or foundries. Another potential challenge for the scalability of this platform is the cost of III–V materials, which is one of the key advantages that silicon photonics holds over traditional native III–V platforms.

Due to the exemplary properties of III–V semiconductors for photonics, plentiful functions can be implemented on the (Al)GaAsOI platform for quantum applications. Besides following the route of SOI in standardizing the basic passive components, (Al)GaAsOI provides several prospective advantages for the monolithic integration of active and passive components. In terms of quantum light sources, the large χ⁽²⁾ nonlinearity can lead to entangled and single-photon generation based on spontaneous parametric down-conversion (SPDC), which is expected to be even more efficient compared to SFWM, further easing the pump power requirements. Similarly, producing squeezed optical states—another essential resource for quantum optical information processing in the continuous variable (CV) regime—can be realized via either the χ⁽²⁾ or χ⁽³⁾ nonlinearities. In addition to the nonlinear processes, one key feature of the material system of (Al)GaAs and its alloys is the compatibility with InAs/GaAs QDs, which can be used for generating on-demand single photons and for achieving single-photon nonlinearities.

By leveraging III–V quantum well or QD epitaxial layers, electrically pumped lasers can be directly integrated along with the passive circuits on (Al)GaAsOI, which can serve as a tunable pump for quantum light generation and an on-chip local oscillator for interferometry. The existence of the EO and piezo-electric effects potentially can enable high-speed modulators with low insertion loss. Importantly, those modulators are suitable to work under cryogenic temperature, which are required for operating QD-based single photon emitters as well as superconducting nanowire single-photon detectors (SNSPDs), which recently has also been successfully integrated on GaAs waveguides [51]. Therefore, a route exists to fully integrated quantum PICs by monolithically integrating all those functions onto (Al)GaAsOI, as shown in figure 7.

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To further improve the scalability, (Al)GaAsOI can be heterogeneously integrated onto SOI PICs to harness large-scale CMOS compatible production. Another strategy to lower the cost of III–V materials is direct epitaxial growth on Si wafers instead of native III–V substrates. Remarkable advances have been made along this direction for the (Al)GaAs material system, whereby the film qualities are comparable with layers on GaAs native substrates.

With the remarkable performance of quantum light sources and the convenience of system-level integration, rapid growth of research in (Al)GaAsOI for integrated quantum photonics is expected. The efficiencies of current nonlinear devices will be further improved, and novel capabilities will be enabled by exploring different properties of the material system. The simultaneous realization of lasers, quantum light sources, modulators, and photodetectors will be the next key steps to accomplish fully integrated quantum photonics with this platform. These developments will also benefit other applications in integrated photonics and it will enable a wide range of new opportunities in classical and quantum computing, communications, and sensing.

We gratefully acknowledge support via the UC Santa Barbara NSF Quantum Foundry funded via the Q-AMASE-i program under Award DMR-1906325. G M acknowledges support from AFOSR YIP Award No. FA9550-20-1-0150 and the National Science Foundation under Award CAREER-2045246.

¹ École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

² University of Technology Sydney, Sydney, Australia

The unique combination of extraordinary physical and optical properties of high-purity single crystal diamond has propelled this material far beyond its traditional use as gemstone in jewellery, fostering a growing body of scientific research in the field of diamond PICs [52]. While PICs made of silicon or III–V materials have reached commercial applications, e.g. in telecommunications and interconnects, quantum PICs are still in their infancy [53]. They notably require on-demand generation of indistinguishable single photons, low-loss optical signal routing, on-chip single photon manipulation and detection, and engineering of specific quantum functionalities, such as quantum registers or quantum memories [54]. In this context, diamond's ability to host paramagnetic, optically active atomic defects [55], such as the nitrogen-vacancy (NV) colour centre [56], has led to its widespread recognition as a promising material for QIP [57]. Diamond PICs have the potential to host large arrays of long-coherence electronic and nuclear spin qubits linked by flying photonic qubits and coherently controlled by microwave circuits [58]. In addition, diamond's unrivalled mechanical properties makes it promising for cavity quantum optomechanics, which provides additional opportunities for implementing quantum coherent frequency conversion and quantum memories in a same platform [59]. As an almost ideal quantum photonic material, diamond holds the promise to combine in a single platform all the required components for large-scale quantum PICs with the potential to operate at ambient temperature (figure 8). To date, an impressive collection of experiments has been realized at the individual component level [60]. This progress has been enabled by the advances in chemical vapour deposition (CVD) growth of single crystal diamond with the level of purity and low defect density required for quantum photonics, and by advances in micro- and nanofabrication, allowing for precision shaping of diamond at the nanoscale [61]. This advancement has recently led to several small scale quantum photonic circuit demonstrations, using hybrid integration of diamond with other photonic material platforms [62]. However, despite these recent achievements, large-scale diamond quantum PICs, with thousands or millions of individual components, remain elusive. This roadmap aims at outlining the requirements for establishing such a platform.

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In order to establish mature and scalable diamond quantum PICs, several challenges need to be addressed, which can be divided into four major areas, namely (a) components, (b) platform, (c) integration, and (d) quantum technology. Over the past decade, an abundance of individual components for integrated diamond photonics has been investigated in academic research. For example, grating couplers, waveguides, phase shifters, power couplers, cavities, optomechanical resonators, SPSs, light emitting diodes, Raman laser, supercontinuum generation and detectors have all been demonstrated [52]. These components have to be matured and their operation optimized for a selected wavelength range; for scalable quantum operation, their insertion loss has to be drastically reduced; finally, they must be combined into a standardized technology. The component-level challenges go naturally hand in hand with the establishment of a platform technology. Building on high quality thin film single crystal diamond as the photonic layer, a manufacturing process flow needs to be developed that can host at the same time passive photonic devices (e.g. couplers, waveguides) as well as active components (e.g. sources, detectors, modulators). The related micro- and nanostructuring techniques need to be transferred from academic settings to foundry-compatible fabrication processes for producing circuits with large quantities of components with high yield. For the construction of large-scale quantum circuits with coherent spin control in thousands to millions of qubits, the most suitable technology approach appears the tight co-integration of electronic integrated control circuitry. While electronic integrated circuits are by themselves a mature technology, this integration challenge requires not only the realization of the physical interface between the electronics and the diamond photonic quantum devices, but also adequate circuit control strategies, which is tightly linked to the development of overlaid quantum protocols and algorithms, and the abstraction from the physical layer into logic and software operation. This full stack integration from the quantum effects in the diamond photonic layer through the physical signal routing, the interface with electronic control towards the quantum protocol can be summarized as the quantum technology challenge.

The outlined challenges to be met for the establishment of diamond quantum PICs require advancements ranging from scientific developments in the physical layer, significant innovations in manufacturing, to implementation of novel concepts in the abstract logical layer, as schematically represented in figure 9. At the diamond quantum photonic component level, further improvement in the coherent control and single-shot readout of quantum degrees of freedom such as individual spin and photon states are required. Electrically driven SPSs, low loss passives and on-chip single photon detectors (SPDs) have to be developed.

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The closely related platform challenge requires significant technology developments. First, advances in material science and engineering are required to deliver high quality single crystal diamond thin films at wafer level. Quantum PICs will require diamond layers with a thickness of a few 100 nm with excellent wafer-level uniformity, low surface roughness, bow and intrinsic stress, as well as excellent crystal quality with low density of defects such as impurities, voids or dislocations. The required innovations in wafer scale growth or layer transfer, polishing, flattening, etching, bonding are far from trivial, and the technology needs to mature in order to achieve required yields. Second, diamond micro- and nanostructuring technologies have to advance, including diamond etch procedures, surface roughness and residual stress control, to achieve excellent dimensional control and photonic performance. Third, embedding optically active spin qubits requires novel approaches in manufacturing, in order to create individual colour centres with few nanometer positioning precision and high yield in a massively parallel way. It would be particularly efficient if future diamond quantum PICs can directly interface with existing telecom infrastructure, such as optical fibers or classical photonic components and integrated circuits, demanding research and engineering on new colour centres or optical frequency conversion.

Integration of the diamond photonic quantum components with their control circuits demands innovative approaches for the photonic-electronic interaction and the engineering of microwave circuits. Finally, the full quantum technology stack has to be addressed in a holistic manner, including abstraction to higher-level programming strategies and the development of optimized diamond photonic quantum algorithms addressing standardization and providing PDKs for accessibility, as has been proven successful in the electronic integrated circuit industry.

Displaying unequalled gleam and internal fire, diamond also exhibits record material properties, that have been thoroughly explored for emerging quantum applications. The unique spin properties of the optically active colour centres in the diamond lattice provide unparalleled prospects for a platform integrating spin, photonic, and possibly phononic qubits. With recent advances in material science, increased availability of high-quality diamond wafers, and progress in micro- and nanofabrication techniques, diamond has now been established as a prime candidate for realisation of integrated quantum photonic circuits with emerging applications in QIP, quantum sensing and single molecule detection. Decades of research generated significant knowledge of the fundamental properties of diamond colour centres and a wealth of optimized nanofabrication protocols. The time is ripe to expedite engagement with industry and foundries to scale these laboratory experiments up to market level.

N Q acknowledges funding by the Swiss National Science Foundation under Grant Nos. 157566 and 183717. C G acknowledges funding by the Swiss National Science Foundation under Grant No. 170684. I A acknowledges the Australian Research Council (via DP180100077 and CE200100010).

Institute of Physics, University of Münster, 48149 Münster, Germany

Optical waveguiding in Ta₂O₅ (also known as tantala) thin films was investigated as early as the 1970s but it was not until recently that Ta₂O₅-on-insulator is emerging as a promising platform for integrated nonlinear and quantum photonics. Ion beam sputter-deposited Ta₂O₅ thin films have been produced with excellent optical properties for several decades, enabling most demanding and timely applications from gravitational wave detection to mHz-linewidth lasers. In integrated photonics, low optical absorption and high refractive index contrast of Ta₂O₅ waveguides on oxidized silicon wafers have yielded propagation loss as low as 3 dB m⁻¹ in CMOS compatible fabrication processes [63]. Notably, compact Ta₂O₅ micro-ring resonators with several million optical quality factors at telecom wavelengths [64] have already been demonstrated, underlining the great potential of amorphous oxides for matching or even exceeding current benchmarks for all waveguide-integrated devices set with significantly more mature dielectric material platforms.

Combining these achievements with the material's wideband transparency from 300 nm to 8 μm wavelength and a third order nonlinear Kerr coefficient of about three times that of SiN, makes an obvious case for exploiting Ta₂O₅ in integrated nonlinear photonics applications. The large bandgap of Ta₂O₅ (3.8–5.3 eV) here outweighs the lower nonlinear refractive index as compared to silicon waveguides, which however suffer from two-photon and free-carrier absorption. Initial work has focused on dissipative Kerr-soliton-based optical frequency combs in the IR spectrum [64] (see figure 10(a)) and supercontinuum generation extending from the IR into the visible range of the spectrum [65] (see figure 10(b)), which benefit from dispersion engineering in thick Ta₂O₅ layers that form without cracks due to the low intrinsic material stress [64]. While these results provide an excellent starting point for integrated nonlinear photonics, Ta₂O₅ has several other intriguing material properties that uniquely benefit integrated quantum photonics. Especially interesting in this regard are the record low thermo-optic coefficient [66], enabling stable operation of high quality-factor devices, in particular at cryogenic temperatures, and the extremely low intrinsic photoluminescence, which is an indispensable requirement when working at the single-photon level.

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The implementation of Ta₂O₅ PICs aims at realizing passive, active, and nonlinear functionalities. Moreover, Ta₂O₅ can host rare-earth ions, including erbium [67], which enables use as a gain medium, thus providing optical signal amplification and lasing capabilities on-chip. While ongoing efforts are mainly concerned with transferring established device concepts to the Ta₂O₅ material system and optimizing performance at the device level, future PICs will increasingly rely on combining several functionalities in a nanophotonic network. This is particularly relevant to integrated quantum photonics, where both scaling to large system size and detrimental effects from photon loss are outstanding challenges.

Essential building blocks of an integrated quantum technology platform will have to include quantum light sources, nanophotonic circuit components and efficient single-photon detectors. The exceptional material properties of Ta₂O₅ have allowed progress with all of these key components. While the generation of photonic quantum states has remained a challenge as yet, the attractive nonlinear properties of Ta₂O₅ offer exciting prospects for producing quantum optical frequency combs [68]. On the other hand, the low intrinsic photoluminescence and optical transparency at visible wavelengths also allows for integrating a wide range of solid-state quantum emitters, such as color centers in diamond [69], with Ta₂O₅ nanophotonic circuits (see figure 11(a)), which had remained elusive for SiN. Moreover, SNSPD seamlessly integrate with Ta₂O₅ waveguides (see figure 11(b)) and provide an efficient, low-noise photon counting solution with excellent timing properties [70]. Importantly for realizing reconfigurable quantum photonic information processing systems, active and passive nanophotonic circuit components have been demonstrated with single-mode Ta₂O₅ waveguides [71]. Directional couplers and multi-mode interference devices with tunable splitting ratios as well as electrostatically actuated phase shifters, as those shown in figure 11(c), show suitability for controlling interference throughout complex, programmable PICs. Lastly, quantum communication (QC) scenarios between remote devices will require efficient optical interconnects, as those in figures 11(c) and (d). Going from the device level to large system size, however, will require minimizing optical insertion and propagation losses across the entire network and accommodating heterogeneous processing techniques.

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Leveraging the full potential of Ta₂O₅ PICs will require more detailed investigation of optical loss contributions from material absorption, impurities and inhomogeneities as well as the influence of design and thin-film processing techniques on waveguide scattering at both IR and visible wavelengths. Importantly for nonlinear optical processes, low loss should be achieved for strongly confined optical modes and Ta₂O₅ thin films of single crystal quality may here offer new perspectives. However, loss studies must also consider cladding materials for which new approaches to minimizing optical absorption may be required, e.g. deposition of deuterated SiO₂-claddings with reduced H-content, which may allow circumventing restrictions arising from the need for annealing Ta₂O₅ at approx. 600 °C for enabling low loss waveguiding.

The longer-term potential of Ta₂O₅-PICs for quantum photonics will to a certain extent rely on the possibility of creating entangled photon pairs as a key resource across all disciplines of quantum technology directly on-chip. SFWM has already been shown in Ta₂O₅-waveguides but nonclassical correlations have yet to be demonstrated. Similar to (quantum) frequency comb and supercontinuum generation, dispersion engineering will play a crucial role for exploring phase-matching conditions that strike an optimal balance between nonlinear parametric gain and loss.

In the short term, the range of functionalities currently available with Ta₂O₅-nanophotonic devices needs to be expanded considerably. On the one hand, the Ta₂O₅-toolbox of active and passive circuit components needs additions from established device concepts such as efficient spectral filters, e.g. for separating pump light from a desired single-photon signal. On the other hand, heterogeneous integration of quantum emitters, active devices and detectors, including operation under cryogenic conditions and from UV to IR wavelengths, will be necessary to enable the full range of quantum technology applications.

In the longer term, these functionalities need to be combined in larger numbers within chip-scale nanophotonic networks. Ta₂O₅ has proven its suitability in semiconductor industry processes but in order to fully exploit the attractive material properties for realizing complex integrated quantum photonic circuits, a concerted community effort will be required for making foundry-type processing capabilities widely available.

Ta₂O₅ offers a combination of material properties that uniquely benefit key functionalities in integrated nonlinear and quantum technology. The fact that extremely low loss performance and a wealth of nonlinear optical effects could be demonstrated at an early stage of developing this material system for nanophotonic applications speaks to the tremendous potential for going beyond state-of-the-art PIC applications. It is particularly noteworthy, that key building blocks of integrated quantum technology are already available on Ta₂O₅-on-insulator chips with much room for future improvement following both intrinsic and hybrid material approaches. The prospect of realizing compact devices with Q-factors reaching billions, low thermo-refractive noise, operation from UV to IR wavelengths and excellent power handling capabilities may suggest that Ta₂O₅ can replace SiN over a wide range of applications [2], however much work remains to be done to turn such visions into reality.

We thank Philip Schrinner, Thomas Grottke and Helge Gehring for their support and discussions on nanophotonic device designs. C S acknowledges support from the Ministry for Culture and Science of North Rhine-Westphalia (421-8.03.03.02–130428).

John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, United States of America

Optical photons have many attractive properties for realization of quantum technologies [53]: they exist under ambient conditions, are generally impervious to environmental noise, and, to an extent, can be generated, manipulated and detected easily. Since they can also travel long distances without significant loss, individual photons are well-suited for quantum key distribution (QKD), which aims to secure messages between distant parties using quantum uncertainty. Yet, these properties of photons also introduce challenges to realize quantum technologies that require deterministic interactions between individual photons, e.g. for photonic QIP.

Integrated photonics will play a crucial role in realizing long- (e.g. worldwide), medium- (e.g. metropolitan- or room-sized), and short-range (e.g. inter- or intra-chip) quantum networks. However, the performance of a photonics platform for quantum technology applications needs to be much better than, and in some ways different from, what is required for classical applications. For example, a quantum photonics platform needs to: (a) be ultra-low loss in order to preserve fragile quantum states; (b) enable precise control of the temporal and spectral profiles of photons; (c) allow fast and low-loss optical switches to route quantum information; (d) be able to operate in visible and telecom wavelengths, where many SPSs and quantum memories operate, and low-loss optical fibers exist, respectively; (e) feature strong nonlinearities for efficient frequency up- and down-conversion, quantum transduction, and entangled photon pair generation; (f) allow integration of photodetectors and operating electronics. Silicon and silicon-nitride, the leading integrated photonic platforms, do not meet these requirements due to the lack of a second-order nonlinearity, which restricts their functionality [53]. Although this could be addressed with crystal modification or heterogeneous integration, it remains to be seen what trade-offs, e.g. in terms of efficiency and scalability, this would encompass.

TFLN has emerged as a promising quantum photonic platform. LN is transparent to optical photons (band gap of ∼4 eV), possesses a strong EO effect, allowing the phase of light to be rapidly varied using microwaves, and has a high second-order optical nonlinearity that can be engineered through ferroelectric domain modulation (i.e. periodic poling) [72]. Importantly, 4'' and 6'' TFLN wafers have recently become commercially available, which have stimulated interest in this exciting material platform.

Breakthroughs in TFLN nanofabrication [73] have enabled the creation of opto-electronic components with performance that surpasses those based on bulk LN, laying the groundwork for developing state-of-the-art photonic quantum processors. These components (figure 12) range from high-bandwidth EO modulators (EOMs) [74], which can enable rapid encoding of qubit states onto light or low-latency routers, to poled waveguides and resonators that convert the wavelength of a photon [75, 76] as well as generate non-classical states of light. These devices are particularly appealing for frequency-domain photonic processing applications that leverage wide bandwidth of optical photons but requires high speed modulators as well as frequency shifters/beam splitters. The latter could be realized using an EO photonic molecule [77, 78], formed by coupling two electrically-driven resonators.

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Among several challenges, one common to all on-chip photonic platforms is propagation loss. TFLN has demonstrated ultra-low optical loss of less than 3 dB m⁻¹ and on/off a chip coupling loss of 1.7 dB/facet using TFLN waveguide tapering [80]. The insertion loss of active EO devices must be considered, often taking into account trade-offs between efficiency and loss when designing the metal electrodes for example.

The bandwidths of TFLN EOMs already exceed 100 GHz and is thus sufficient for many quantum applications. However, further reduction in drive voltages is important, especially when considering realization of multiplexed and dynamic switch networks and gates. These must also be interfaced with large-scale microwave circuitry for precision control and synchronization.

TFLN allows EO control of optical photons without any additional uncorrelated optical (noise) photons being induced by the (low-energy) microwave field. However, optical frequency conversion is accompanied by additional noise photons, e.g. due to Raman processes, which must be suppressed for single photon-level operation. Such conversion is important for interfacing telecommunication-wavelength photons with visible-wavelength devices, e.g. Si photodiodes and quantum memories. For that matter, TFLN circuits which operate at wavelengths out of the infrared must be further developed beyond that shown in proof-of-principle demonstrations. This would also benefit quantum state generation by way of nonlinear processes such as SPDC, which can convert a visible photon into two telecommunication wavelength photons, and squeezing.

Heterogeneous integration of devices with TFLN, an exciting prospect to realize high-bandwidth photonic interconnects between hybrid systems, is still in its infancy. Hybrid systems include acousto-optics, SPDs, or atomic interfaces on TFLN. The latter could be QDs,color centers, or rare-earth ions, of which could act as SPSs or mediate photonic gates. SPDs on TFLN must be improved beyond that shown in initial demonstrations, e.g. with respect to efficiency (46%) and timing resolution (32 ps) [81], while also sourcing feed-forward signals for control of later operations.

Finally, full integration of all functionalities must be realized (figure 13). This is especially challenging for quantum circuits that require high-contrast interference, meaning no distinguishing information about a photon may be introduced by the devices. Chips must be robust to environmental disturbances, e.g. heat generated at electrodes, and operate over long periods of time in order to allow statistically relevant measurements. The latter could be problematic due to photorefraction in LN [72], which is a change of refractive index with high laser intensities, e.g. during optical frequency conversion.

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Along with device demonstrations and improvements, photonic loss must be reduced to the levels of the material limit, which is 0.1 dB m⁻¹ for LN. This could allow optical nonlinearities at the single photon level inside ultra-high-Q TFLN resonators. Large waveguides will help in this regard by ensuring the optical mode does not interact with the rough sidewalls that are introduced by etching, but this will reduce the interaction strength with LN, and hence reduce device performance. Sidewall loss can be mitigated with further optimization at the etch step, e.g. using purer chamber gases or improved removal of re-deposited material during dry etching. The role of surrounding materials must be carefully examined, including absorption or surface chemistry from deposited oxides. Further, imperfections from the TFLN production process, such as surface roughness or impurities can be addressed by polishing and annealing. Material improvement itself must be investigated, including stoichiometric or doped TFLN, including magnesium doping which will reduce the impact of photorefraction. These improvements must be consistent across the wafer and be repeatable.

Other fundamentals, such as improving the EO bandwidth of modulators must be undertaken. For resonator-based modulators, this bandwidth is restricted to tens of GHz by the width of the optical resonance and resistance-capacitance limit of the electrode. Traveling-wave modulators allow bandwidths into the hundreds of GHz using optimized velocity and impedance matching between microwave and light. The role of piezoelectric loss should also be accounted for. Among other improvements, poling precision, uniformity, repeatability, and scaling must also be addressed. Shortfalls of TFLN must be overcome with suitable heterogeneous integration, e.g. integration of diamond color centers or by leveraging microwave-frequency quantum acoustics.

We are currently only beginning to see the potential that TFLN can provide to develop quantum photonics. Further steps must be taken to realize advanced and fully integrated quantum functionalities at scale. This will critically advance emerging quantum technologies, in particular quantum networks, and will result in improvements to devices used for classical photonics and telecommunications. Going forward, we expect light to play a significant role in quantum technology due to its ability to carry large amounts of frequency-multiplexed qubit information in a single spatial mode, which will allow the redundancy needed to overcome system loss and errors with a lower scaling overhead. Thus, focus should be placed on creating and improving light-matter qubit interfaces, a task well-suited to TFLN.

N S and M L thank Bart Machielse and Ben Pingault for manuscript comments, Boris Desiatov for the illustration shown in figure 13, and the rest of the Lončar group for discussions. N S acknowledges support by the NSERC, INQNET research program, and by the DOE/HEP QuantISED and QCCFP programs. M L acknowledges support by NSF, DARPA, ARO, AFRL, ONR, AFOSR and DOE.

Tin Komljenovic¹, David Weld² and John E Bowers²

Status

Quantum science is a field at a technological inflection point. Recent advances in control and readout of quantum bits have underscored the spectacular promise of QIP [82, 83]. However, this promise will only be realized if the current laboratory successes mature into a fully integrated approach. In the development of classical information processing, the transistor represented a crucial advance, but equally important (and meriting a separate Nobel prize) were techniques for assembly and integration of heterostructures, leading to the integrated circuits which pervade our world today. Synthesis and assembly of integrated quantum platforms is a grand challenge which will require contributions from a diverse range of fields. Photonics will play a key role in this effort, thanks not only to the maturity and power of photon manipulation technologies but also to the unique quantum mechanical properties of the photon.

Visible light photonics is an area of particular importance, due to the typical energy scale of transitions in the atoms and ions that comprise a key element of quantum technology (see figure 14). An atom is the paradigmatic quantum mechanical system. The precise tools of atomic spectroscopy that gave birth to quantum mechanics have evolved into tools of control, allowing experimental access to all internal and external degrees of freedom and enabling, for example, the realization of states of matter in which millions of atoms occupy a single quantum state at nanokelvin temperatures. The precision and control available in such atomic physics experiments makes them a promising platform for QIP and also an ideal tool for quantum-enhanced sensing, navigation, and timekeeping.

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A key bottleneck in the development of atom-based quantum technology is the complexity of laser sources and associated optical hardware. Modern atomic physics began with the invention of the laser and has always depended upon it. As experiments grow more complex, involving for example molecules or multiple independently addressed atomic elements, the need for individually controlled laser sources at numerous distinct frequencies has limited scalability and restricted commercial applications. Integrated photonics will overcome this challenge and realize the potential of quantum technology [10, 15].

Current and future challenges

Advances in science and technology to meet challenges

Depending on the approach, multiple advances are needed to enable chip-scale optical sources meeting the requirements of next generation quantum technology-based sensing systems. Improvements in active materials (e.g. direct gain in green-yellow range) and passive materials (low loss, especially in the UV-blue range) can enable path for wafer-scale integration in full wavelength range. In the case of non-linear generation, improvements in heterogeneous integration to enable higher contrast waveguide geometries can increase efficiencies by reducing the mode volume. At the same time, processing has to be improved as phase matching generally requires very precise control of waveguide dimensions. The use of multiple materials can place additional restrictions on the processing thermal budget due to different coefficients of linear thermal expansion, which can be especially important when defining metal contacts. Once material related limitations are addressed, optical coupling between various materials has to be optimized. The main challenge is to facilitate efficient optical coupling between dielectric materials with refractive indices generally in the range of 1.45–2.2, and semiconductor materials that can provide gain and/or efficient non-linear conversion but typically have refractive indices in the range of 2.3–3.6. Such large difference in refractive indices, in case direct adiabatic power transfer is designed, requires narrow taper tips.

Many of said challenges are being actively addressed with recent demonstration of heterogeneous integration of GaAs lasers on SiN waveguides [87] where efficient coupling between materials with refractive index larger than 1.5 was demonstrated and is shown in figure 15.

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Concluding remarks

Acknowledgments

University of California San Diego, La Jolla, CA 92093, United States of America

Entanglement is a useful resource in quantum networks. Entangled-photon sources play a crucial role in realizing such networks, similar to lasers in classical data networks. Similar devices can also be used to generate heralded single-photon states and squeezed light. Integrated photonics can generate and manipulate quantum states of light in a scalable and efficient way [53, 88–90]. Entangled photons can be generated from QDs without fine-structure splitting, as well as from optically-pumped nonlinear devices which use SPDC or SFWM. Figure 16 shows some of the popular photonic materials choices and devices formed using them towards the major goals of current research in chip-scale entangled-photon sources. In-depth progress reviews are presented elsewhere [91–94]. Here, we will mainly focus on SPDC and SFWM devices which can be easily realized at the micro-chip scale using simple dielectric or semiconductor materials, and the devices do not require cryogenic cooling.

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When pumped with continuous-wave light, the signal and idler photons are entangled in a time-energy basis, if the joint spectral intensity (JSI) of the signal and idler photons is not separable. To realize a heralded source of pure, indistinguishable single photons, a separable JSI can be engineered through device design and adjusting the properties of the pump pulse. When the device is pumped with a sequence of closely-spaced short pulses, entanglement in a time-bin basis is created. By using various waveguide components such as beam splitters, polarization rotators and frequency shifters, entanglement can be created in the spatial, polarization, mode and frequency domains as well. Higher-order entanglement (dimension d > 2) allows for more information (qudits) to be transported by photons, which are inevitably lost due to absorption, scattering or diffraction during propagation [95]. Since scalability of on-demand entangled-photon sources has not yet been realized, current practice relies on multiplexing probabilistic pair sources through linear optical gates and post-selection [6, 34], but other schemes have been proposed [96].

Recent advances in device fabrication techniques have led to the ability to lithographically create highly-confined waveguides and compact micro-resonators, which enables precise dispersion engineering [97]. For quasi-phase matching (QPM) through periodically-poled thin-film materials, a combination of electron-beam lithography and optical lithography has been used to precisely define electrode structures for short-period poling [98], which has benefits in classical nonlinear optics as well. Table 2 compares two approaches for room-temperature entangled photon sources, those based on the χ⁽²⁾ optical nonlinearity and those using χ⁽³⁾, from an integrated photonics perspective.

Although the χ⁽²⁾ nonlinearity used in SPDC is absent in un-strained Si and SiN, the weaker χ⁽³⁾-based SFWM nonlinearity can be enhanced by using micro-resonator and coupled-microresonator devices [99–101]. To achieve entanglement generation rates that are comparable to χ⁽²⁾ devices and comparable QD technology, it is critical to achieve a high quality factor Q_loaded >10⁵ since the pair generation rate scales with the third power (approximately) of the quality factor, while also supporting a high pump power. The pump and entangled photon pairs can be placed within the telecommunications wavelength range, where low-noise pump laser diodes and filters are readily available. A dual-pump SFWM process can be used to generate frequency-degenerate signal and idler photons, with some additional considerations for noise management [102]. In contrast to fiber or SiN sources, the Raman noise contribution in Si SFWM is narrowband, and spectrally well separated from the pump. Silicon microelectronic components can be incorporated in, or used with, silicon photonic structures, such as p-i-n diodes fabricated across the waveguide cross-section for resonance monitoring [103], and step-recovery diodes which generate short pulses using a continuous-wave RF input, and can drive an EOM for shaping optical pump pulses [104]. Out-of-band laser light transmission can be used for stabilization [34]. To help realize pure heralded single-photon states, different waveguide-resonator coupling coefficients are needed for the pumps, and for the signal or idler photons. Since the wavelengths are similar in SFWM, a more sophisticated coupling structure may be useful, such as the two-point interferometric couplers [105].

While it is possible to induce a weak χ⁽²⁾ effect in centrosymmetric materials, it is also possible to bring the stronger χ⁽²⁾ effect of SPDC in LN into silicon photonics ecosystem, for example, by using TFLN and bonding. SPDC requires a short-wavelength pump; however, low noise 775 nm pump diodes are common, although microchip-scale short-pulse lasers at these wavelengths are not yet widely available. Because of the small waveguide cross-sectional area, significant performance benefits can be achieved in comparison to traditional SPDC waveguides in LN [98, 106]. Waveguides in TFLN have a high group-velocity dispersion, and therefore require a shorter QPM poling period. Traditional SPDC requires ultrashort optical pump pulses generated by a mode-locked laser, which is difficult to integrate monolithically [107]. Although dispersion engineering over wide wavelength spans is challenging, TFLN and other χ⁽²⁾ materials can also be used in the micro-resonator configuration, achieving very high nonlinear efficiencies [108].

Improving the heralding efficiency for pure single-photon states

Multiplexing

Compatibility of sources with quantum memories

Entangled photon-pair source devices are now available from research and commercial sources, similar to crystals for other nonlinear optics applications such as second-harmonic generation and wavelength conversion. However, they will not meet the needs for building a future scalable quantum network. Aside from the technical performance limitations, many traditional designs do not generally benefit from modern silicon-based microfabrication, which can realize hundreds or thousands of devices on a wafer. While silicon photonics is obviously (mostly) compatible with silicon microfabrication in industry, other integrated photonics approaches which offer better performance may also be compatible with the silicon industry, including χ⁽²⁾ materials such as LN. A quantum photonics designer can now benefit from a variety of engineering ideas, such as heterogeneous bonding, pick-and-place assembly and transfer printing, post-fabrication trimming and reprogrammable photonic circuits. Together, these advances will comprise a much richer set of tools with which to address the grand challenges of building low SWAP (size, weight, and power), low-cost, manufacturable and high-performance entangled-photon sources for large-scale entanglement distribution and error correction in quantum networks and QIP.

This work was supported by National Science Foundation (NSF) (EFMA-1640968), NASA, Sandia National Laboratories, United Technologies Research Center, Keysight Technologies and IBM.

National Institute of Standards and Technology, United States of America

Similar to the NV center in diamond, there exist many different emissive centers in the silicon lattice. These silicon emissive centers (SECs) were characterized extensively in the 1980s [113], and underwent a resurgence in popularity in the 2000s by groups looking to develop silicon lasers for telecommunications applications [114]. While there was one report of the lasing G center, a carbon-based SEC, work on SECs for the development of lasers has largely been abandoned. Many SECs are only luminescent at cryogenic temperatures, which is unappealing to the telecommunications industry, but an accepted part of quantum technologies. SECs have been relatively underexplored for QIP as they must emit below the silicon bandgap, where the most efficient APDs are insensitive. The increased availability of superconducting single-photon detectors has finally allowed the study of quantum SECs.

Many SECs form states within the bandgap of silicon, allowing electrical injection. Several electrically-injected all-silicon LEDs have been demonstrated, including an electrically-injected waveguide-coupled cryogenic optical link with a W center (silicon interstitial based SEC) LED [115] (figure 17(i)). The W and G centers exhibit some of the brightest emission of any SECs, and are promising as SPSs. In the past year, first measurements of single-photon emission from G centers have been reported [116, 117], and single SECs across the telecom wavelength range have also been observed in carbon-implanted silicon [118]. A silicon photonic spin-donor qubit quantum computing platform has recently been proposed [119], with the idea of using photonic coupling between chalcogenide spin qubits in silicon (figure 17(ii)). Spin qubits in silicon have exceptionally long coherence times due to the availability of isotopically pure silicon. Isotopically pure silicon has also been shown to favorably impact the linewidths of some SECs [120]. The spin–photon interface in silicon, could it be realized, would therefore have significant advantages both due to this property and the advanced fabrication capabilities available in silicon. Rare earth SECs, with very stable emission across crystalline hosts, have also been investigated for quantum applications. Rather than using optical emission, which has a very long lifetime, optical addressing of a single Er ion in silicon has been demonstrated, in conjunction with the injection of a single electron spin for manipulation [121].

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Generation of SECs is usually performed by ion implantation followed by annealing. For many SECs, the process leaves significant damage in the crystal lattice, causing unintentional introduction of non-radiative recombination centers. The structure of many SECs and these non-radiative centers are also often poorly understood. The emission from single G centers that has been observed so far showed strong inhomogenous broadening. Ion implantation processes may generate many different types of SECs, offering opportunities but also challenges to develop processes that only create the SECs of interest [118]. For many applications, placement of individual SECs will also be necessary. For SPSs, there are several remaining challenges. The long radiative lifetimes of SECs lower the quantum efficiency due to competitive non-radiative processes, as well as reducing the maximum repetition rates. Single-photon emission has only recently been observed from G centers and SECs in carbon-implanted silicon, while single-photon emission still remains elusive for many other SECs interest. The most promising SECs may emit in the mid-IR, a technologically challenging wavelength range. From the point of view of an electrically-injected SPS, the ability to inject a single electron on-demand and generate indistinguishable single-photons is a holy grail, but work is still needed to develop the types of structures needed for this. The spin–photon properties of several types of SECs have been investigated, including Se, Mg, as well as the G, W and T centers (all based on interstitial silicon complexes either with or without carbon). It appears that the Se+ and T center are both promising as a spin photon interface, while the right energy level structure has not yet been observed in other SECs. A host of SECs remain unexplored, and it is likely that the perfect SEC for the application has yet to be identified. For a spin–photon interface, the emitters must be strongly coupled to a photonic cavity. This requires the development of a system of photonic cavities all on-resonance with the emitter zero phonon line, and with each other.

Despite research in this area ongoing since the 1970s, the optimal conditions for generation of specific SECs, the physics of formation of many of the most common SECs, and the sources of non-radiative recombination are not well understood. Techniques such as atomistic simulations, variable energy positron spectroscopy, and Rutherford backscattering could help elucidate some of these properties. More study on the quantum properties of different SECs is ultimately needed. The main improvements in technology needed are improved detectors in the infrared, and ultra-low-loss integrated photonic elements in the mid-infrared. Coupling of W centers to microresonators has been demonstrated recently [122] (figure 17(iii)), but Purcell enhancement and strong coupling of SECs to photonic cavities are still awaiting experimental demonstration, despite indications that this is well within reach of silicon photonic microresonator technology. Purcell enhancement could overcome the long radiative lifetime that is characteristic of many SECs. It is unclear what effect the presence of the etched surfaces introduced by these cavities will have on the performance of SECs, and advances in our understanding of this effect are needed. For a photonic spin–qubit interface, a mechanism for overcoming homogeneous and inhomogeneous broadening of the emitters, such as electrical tuning, is needed, as well as tunable high-Q low mode-volume silicon photonic cavities for matching resonant wavelengths of cavities to each other and to the emitters. Placement of SECs with atomic-level precision will also be needed; this has been demonstrated with spin qubits in silicon based on phosphorus donors, but may be much more challenging for complexed SECs involving multiple atoms. For useful electrically-injected SPSs, a first demonstration of electrically-injected single-photon emission is needed, as well as a mechanism for resonant electrical injection for to ensure the generation of indistinguishable photons. The technologies used for single-electron injection and optical addressing of spin qubits in Er ions may prove useful in this case. With major technological developments, there is also the potential for SECs to contribute to quantum technologies in other ways, such as an electrically-injected cryogenic silicon laser to pump on-chip pair sources, or as an optical interface from cryogenic to room temperature.

Emitters in silicon show promise for quantum technologies on several fronts. First, they may lead to silicon-compatible electrically-injected single-photon emitters, potentially enabling a wide variety of quantum information experiments. They may provide a spin–photon interface for a system with very long coherence time spin qubits, allowing a mechanism for long distance coupling between qubits. However, for these technologies to become a reality, the right defects must be identified and studied, and the photonic and electrical interfaces needed must be developed.

This is a contribution of NIST and not subject to copyright.

University of California Davis, Davis, CA 95616, United States of America

SiC has attracted attention of the photonic and spintronic communities since 2010 when it was proposed as an alternative wide bandgap defect host to the prominently researched diamond, with an outlook of improved optical stability and industrial maturity. The advantages of SiC as a substrate included wafer-scale availability, presence of the second order optical nonlinearity, and easier opto-electronic integration, however, its color center properties were yet to be explored. Throughout last decade, research on divacancy and silicon vacancy (SiV) centers (predominantly in 4H-SiC polytype) demonstrated microwave and phonon driven coherent control of the electron spin, millisecond spin-coherence times (even without isotopic purification), indistinguishable single-photon emission, and, moreover, photonic and optoelectronic device integration. These results set SiC on a promising path to defining the quantum technology backbone for applications in QC and computation (figure 18).

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While greatly benefiting from being a solid-state platform in terms of scalability, the optically active defects take a hit in performance due to the interactions with lattice vibrations. Overcoming this limit, the integrated color center photonics in SiC leads to both an improved, as well as a paradigm shifting, performance of quantum emitters. Placing SiV into a nanopillar [123] has shown increased light collection needed for more precise optical readout of a spin–qubit, while its integration with nanocavities has resulted in Purcell enhancement of light emitted into the zero-phonon line (ZPL) [124, 125] needed for high fidelity indistinguishable-photon operation in quantum applications. Strong cavity quantum electrodynamical coupling of one or multiple color centers to a nanocavity has been proposed for high-speed quantum light sources, as well as for the generation of hybridized light-matter states that play a key role in photonic quantum simulation [126]. Due to their small inhomogeneous broadening and nanodevice scalability, color centers are poised to overcome the stalled progress in a variety of quantum photonic geometries whose realization has proved impractical to atomic and QD systems.

The deployment of fiber-based quantum networks would benefit from a presence of telecommunications range quantum emitters. While Si vacancy and divacancy in 4H-SiC provide longer operating wavelengths than diamond defects and QDs, emerging SiC color centers, such as the NV [128, 129] and the vanadium center [130], are currently explored in the range 1300–1550 nm.

A major color center integration challenge is the incompatibility of well-defined defects with thin heteroepitaxial films. Most SiC polytypes do not grow on sacrificial substrates, except for cubic layers of 3C-SiC grown on silicon whose lattice mismatch prevents formation of narrow-linewidth color centers. This leaves no easy avenue for providing refractive index contrast between a structure and its surrounding, needed to confine light in nanodevices. Nevertheless, several successful directions have been pursued: photo-electrochemical etching [124], SiC thinning and bonding onto an insulator [125], and Faraday-cage angled etching [131]. These promising approaches are yet to be developed into wafer-scale arbitrary substrate processes needed for commercialization of quantum technologies.

Another exciting and complex challenge is the realization of a high-fidelity spin–photon interface using a color center with long spin-coherence time, essential to quantum repeater development and cluster-entangled state generation [127]. This task requires (a) a color center with a suitable entanglement scheme, (b) optimized coherence achieved via intrinsic symmetry of the defect, isotopic purification of the substrate, magnetic field nuclear bath dilution, or dynamic decoupling control, (c) integration into a low-loss nanocavity with a favorable dipole orientation which would strongly promote the no-phonon radiative emission, (d) efficient light coupling into an objective lens or an optical fiber.

To meet the challenges in photonic quantum simulation, collective coupling of nearly-identical color centers to a common nanocavity is to be demonstrated. Nanofabrication techniques that can both produce low-loss nanocavities and maintain low strain in the substrate are needed to achieve light-matter coupling in the cavity-protected regime which would enable exploration of polariton physics [126].

Finally, fabrication of SiC color center photonic devices with superconducting detectors on the same chip would enable fully integrated photonic quantum circuits with applications in quantum computing. The advantage of such approach compared to the competing methods are the long coherence, connectivity and scalability of qubits.

Promising experimental results on NV center generation and coherent manipulation [132], as well as theoretical proposals for their spin–photon interfaces have been demonstrated in SiC [127]. Integration of these telecommunications range emitting centers into nanophotonic devices, as well as an increase of their spin-coherence, is a work in progress. Applications in the proposed high-speed long-distance QCs, and measurement-based quantum computing (MBQC), are likely to follow.

To meet the wafer-scale and arbitrary substrate nanofabrication needs, ion beam angle-etching approaches, similar to those developed in the diamond platform, are to be explored. These methods can be used to accelerate the progress toward achieving high-Purcell enhancement, cavity quantum electrodynamical interaction, as well as bipartite and cluster entanglement.

A proof-of-principle coherent control of a Purcell enhanced divacancy in 4H-SiC was recently demonstrated in a suitably doped substrate [124]. The generalization of this method to other substrates and color centers potentially offering longer spin-coherence times and alternative wavelengths needed for versatile quantum hardware development will make for an impactful step toward quantum hardware integration.

Demonstration of indistinguishable photon emission from a single SiV [133] represents an excellent steppingstone toward both multi-emitter entanglement and cluster-entangled state generation. Extending this experiment to color centers integrated into nanocavities would increase the fidelity of entangling processes. Localized wavelength tuning implemented via strain, electric field or Raman scattering would enable entanglement of photons emitted from different color centers.

Recently, the first SNSPDs on 3C-SiC substrate were implemented [134]. Further exploration with substrates that host color centers, as well as the integration with prefabricated photonic circuits, would help meet the quantum computing frontier.

Due to the SiC's commercial presence in power electronics and MEMS, expansion of industrial involvement into quantum applications, including commercial availability of isotopically purified samples, SiC on insulator platforms and in-situ doping of desired defects, is expected to propel further research and development.

A decade of investment into the exploration of optically active defects in SiC has borne a frontrunning platform for commercial integration of quantum hardware. With further advancements in substrate processing, photonic design, and optical and microwave control, SiC photonics and spintronics are poised to form the quantum technology backbone that supports key processes across all flavors of QIP.

This work is supported by the National Science Foundation (CAREER-2047564).

Technische Universität Berlin, Berlin, Germany

Quantum light sources, which emit photons in the telecom windows at 1.3 µm (O-band) and 1.55 µm (C-band), are basic building blocks for fiber-optic-based QC over long distances. Generally, the single-photon character can be approximated comparatively easily by attenuated lasers. However, the emission statistics of attenuated lasers is intrinsically of classical nature, which prevents their use in advanced QC approaches. In contrast to this, solid-state quantum emitters can generate individual photons in principle on demand [135]. In this context, high quality semiconductors QDs are of great interest and can be produced in a self-organized manner using modern nanotechnology processes. In fact, GaAs and InGaAs QDs emitting at around 780 and 930 nm are among the best single-photon emitters today. InGaAs QDs can also be designed for emission at telecom wavelengths. For this purpose, the difference in lattice constants between InGaAs and GaAs must be reduced by suitable measures. For emissions at 1.3 µm, the method of strain reducing layers has been established and optimized [136], while metamorphic buffer layers are used for emission at 1.55 µm [137]. Alternatively, InGaAs QDs at 1.55 µm can also be realized using InP substrates [138]. In all cases, SPSs with narrow linewidths and high multi-photon suppression could be demonstrated. It was also possible to develop electrically driven entangled photon pair sources based on 1.55 µm QDs and to use them for fiber-based QC [139].

Despite the enormous technological advances in the development of telecom quantum emitters, there are still many challenges and open questions that must be solved in order to open up the envisaged fields of application in photonic quantum technology. With respect to device fabrication, it is important to go beyond proof-of-principle results and realize single quantum emitter SPSs in a controlled manner and with a high process yield. This is a challenging task because the used self-organized growth process leads to randomness in the position and emission wavelength of individual QDs, which leads typically to process yields in the few percent range. With respect to the brightness of the sources, it is important to increase the photon extraction efficiency significantly from <40% achieved to date [140] to values beyond 90%. A promising approach for this is the (deterministic) integration of QDs in circular Bragg gratings (CBGs) in combination with a gold mirror on the back which promises photon extraction efficiencies >95% and Purcell factors close to 30 [141]. In addition, for the future application of SPSs as modular building blocks in photonic quantum technology, efficient on-chip coupling to single-mode fibers is essential. It is technologically very demanding to implement such a coupling: It requires not only a robust mechanical alignment with sub-µm accuracy, especially for the often-required cryogenic temperature operation, but also an optical mode-matching between SPS and fiber. In addition, increasing photon indistinguishability to values beyond 90% is of great importance for QC applications. In fact, so far the photon indistinguishability of telecom QDs has been limited to less than 20% without temporal postselection [136, 140]—a very problematic issue which is attributed to the non-ideal crystal quality of the QDs and their surrounding semiconductor matrix and material interfaces in case of heterogenous device concepts. Finally, a very precise control and stabilization of the quantum emitter's wavelength on the order of the homogenous linewidth is essential for applications that are based on entanglement swapping through Bell-state measurements.

Extensive technological developments are necessary in order to solve the diverse challenges towards ideal telecom SPSs (figure 19). First, it is of paramount importance to maximize the optical quality of the emitters themselves in terms of their emission linewidth, coherence and indistinguishability. In the field of semiconductor QDs, this primarily affects epitaxial growth. Here it is certainly necessary to sensitively optimize the layer design and the growth parameters in order to increase the optical quality of the QDs via structures with reduced defects—or to develop revolutionary novel growth concepts for telecom QDs. Here, Hong–Ou–Mandel measurements on photon indistinguishability, which is a very sensitive probe regarding the detrimental impact of defect states etc, can provide important feedback for iterative optimization of the QDs. Beyond that resonant excitation schemes like resonance fluorescence and two-photon resonant excitation need to be established and optimized as experimental tools for the maximization of the photon indistinguishability. Concerning the randomness associated with the typical self-assembled realization of many types of quantum emitters and the resulting poor process yield, it is important to develop and apply deterministic nanofabrication technologies. Among them in-situ electron beam lithography is very attractive and has to be adopted and optimized for the deterministic device integration of telecom quantum emitters. First results in this direction have recently been published in [136], but further refinements are required to deterministically realize for instance telecom QD-SPSs that are based on CBG structures. In connection with this, it is important to develop efficient and precise techniques for the spectral control of the quantum emitters. In this context, the spectral strain tuning via attached piezo elements that are electrically controlled is extremely attractive. This technology has already been used very successfully for QDs with emission <1 µm and could recently also be demonstrated for deterministically fabricated QD-SPS in telecom O-band. In recent years, very interesting technological approaches for on-chip fiber coupling of QD-SPSs have been developed. Published results rely either on optical alignment in combination with gluing the fiber [142] or on micromechanical fiber holders and micro-optics [143, 144]. Based on these initial successes, further technological developments must follow in order to significantly increase the photon coupling efficiency from a few percent achieved to date to values beyond 90%, for example using CBGs [141].

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Quantum light sources with emission in the telecom O- and C-band are among the most important building blocks for the implementation of fiber-based quantum networks, which can pave the way for the global quantum internet. Based on existing results, QD-SPSs are very promising candidates for meeting the diverse requirements of these application scenarios. In the future, it will be crucial to develop modular stand-alone SPSs with the highest photon coupling efficiency and the best possible quantum properties, which can be conveniently integrated into quantum networks.

Financial support from the European Regional Development Fund of the European Union via the FI-SEQUR project and from the German Research Foundation through CRC 787, Re2974/23-1 and Re2974/24-1 is gratefully acknowledged.

¹ John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, United States of America

² QuTech, Delft University of Technology, Delft, The Netherlands

³ Department of Physics, Harvard University, Cambridge, MA 02138, United States of America

⁴ These authors contributed equally.

Over the past decade, color centers in diamond have been explored with the goal of utilizing their optically accessible spin for the implementation of quantum photonics and quantum networks [57, 58]. These networks could be constructed from a series of nodes comprising color centers embedded in nanophotonic cavities, connected to each other via telecommunications fibers. The nodes act as quantum repeaters and processors, and enable novel, optically mediated entanglement topologies over distances for which photon loss would make direct transmission of entanglement impossible. Realization of such a network would enable technologies such as long distance QKD, distributed quantum computing, and enhanced long-distance quantum sensing [57].

Several breakthroughs towards this goal have already been achieved utilizing two primary color centers, the negatively charged NV center (see figure 20(a)) and the negatively charged SiV center [58] (see figure 20(b)). The NV center has been used to demonstrate loophole-free, photon-mediated entanglement between distant spins [145], as well as deterministic delivery of entanglement at a rate which exceeds the decoherence rate of the entangled state [146]. In parallel, the coherence properties of the NV spin have been improved to over a second [147]. Neighboring nuclear spins have also been harnessed through the NV spin as long-lived ancilla qubits and memories culminating in the realization of a 10 qubit quantum register and entanglement of 7 qubits [148].

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More recently, the SiV center has attracted interest due to its superior optical properties [58]. In particular, the SiV maintains its charge and spectral stability when integrated into nanophotonic cavities. This property has enabled the realization of an integrated, SiV-controlled single photon switch [60], coherent interaction of two SiV spins through the optical mode of a photonic cavity [149], and memory-enhanced photonic Bell-state measurements [150] (see figures 21(a) and (b)). The cooperativity of the spin–photon interface enabled by the nanophotonic cavities now reaches above 100, thus indicating reliable coupling between itinerant photons and the SiV spin memory. Tapered waveguides allow the extraction into an optical fiber of more than 90% of SiV photons emitted into waveguides (see figures 21(a) and (b)). Integration of nanophotonic devices comprising SiV color centers with mechanical devices [151] and nonlinear optics platforms has also been demonstrated [9].

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Both the NV and SiV platforms have demonstrated the individual components required for the creation of quantum networks with quantum repeaters (see figure 21(c)), and are now pursuing integration of the required technologies and enhancement of optically mediated entanglement rates.

The highest rate of photon-mediated entanglement between two NV center spins is currently 39 Hz [57, 146]. This rate is limited by the 4% probability that the NV emits photons into its ZPL (see figure 20(a)) and by a limited collection efficiency. This can be addressed by embedding NVs into optical cavities, which in the case of fiber cavities has enabled a ten-fold Purcell enhancement [152]. Further integration requires the use of nanophotonic cavities fabricated directly in diamond, which is hampered by spectral instability of the NV near surfaces [153].

Such nanophotonic cavities, as successfully used for SiV experiments (see figure 21(b)), remain difficult to fabricate due to the lack of techniques for heteroepitaxial growth of pure, single-crystal diamond. Instead, several techniques have been used to undercut devices in bulk diamond [153]. Among these, crystallographic and angled etching are the most promising, but can produce only specific device topologies.

Furthermore, to enable large spin–photon coupling, photonic cavities rely on small mode-volumes. Reproducibility remains a challenge for such cavities due to the limited precision with which color centers can be localized through implantation and due to fabrication-induced damage. Crystal damage also causes spectral instability and inhomogeneity between centers [153]. This is a limiting factor in scaling up to larger networks, as photons most easily couple emitters with the same transition energies.

The design of larger networks will also require color centers to be integrated into or coupled to other photonic platforms for photon routing, manipulation, and conversion to telecom wavelengths [9, 154]. Further integration with other quantum computing platforms, such as superconducting qubits or trapped ions, will be beneficial to hybrid approaches to QIP.

Finally, much progress could be made through the search for novel color centers combining superior spin and optical properties [154]. These properties can include high photon yield into the ZPL with near unity quantum efficiency, long spin coherence times with optical addressability at elevated temperatures, or low sensitivity to strain, charge and magnetic noise.

Ongoing theoretical and experimental research efforts have led to several proposed solutions for the challenges facing diamond color center-based quantum networks.

Of primary interest is improving the understanding and control of the elements that impact the inherent properties of color centers. This is especially important for the NV center, but would also contribute to the development of new surface treatments, implantation techniques, annealing parameters, growth conditions, and novel strategies such as shallow implantation followed by overgrowth that could improve the properties of all forms of color centers [153].

Narrowing the range of novel emitters that need to be explored experimentally requires a systematic understanding of the desired properties of emitters and further improvement of computational methods for evaluating candidates [155]. The related efforts into reducing the cost and improving cooling power of cryogenic technologies are also important for increasing academic and industrial access to new color center technologies.

The improvement of cavities for spin–photon interfaces and their integration with new technologies requires progress in fabrication techniques. The most developed fabrication strategies rely on undercut photonic devices that can still be optimized further, while novel techniques involving the use of suspended diamond films that could enable more straightforward device fabrication require more investigation. Future diamond platforms should also continue to integrate microwave, acoustic, and electromechanical functionalities as control mechanisms for color centers [151, 153]. Improving access to ultrapure diamond substrates and facilities for overgrowth of existing substrates remains an ongoing and important effort.

The parameter space of existing techniques for nanophotonic device design also remains underexplored. Larger mode volume cavities could be coupled to NV centers, overcoupled or ultrasmall mode volume cavities could enable higher cooperativity or more efficient spin–photon gates, and inverse design techniques could be used to enable more sophisticated device properties [153, 156].

Finally, permanent packaging of diamond photonic devices that allow simultaneous addressing of multiple color centers will be essential to large scale integration. This could be accomplished by permanent splicing of fibers onto existing devices, pick-and-place integration with other platforms [9], or flip-chip technology [153].

Driven by progress in nanofabrication, theoretical understanding, and experimental sophistication, diamond color centers coupled to nanophotonic devices have emerged as a leading photonics and QC platform. Technology surrounding the NV center has progressed furthest, resulting in demonstrations of long distance entanglement. The entanglement rates could be boosted to technologically relevant levels with the development of techniques for integration of the color center with cavities. The SiV center has been successfully integrated with nanofabricated cavities, has been used to demonstrate enhancement of QC rates, and is progressing rapidly towards similar demonstrations of long distance entanglement. Meanwhile, ongoing research into other color centers could lead to the discovery of emitters which can combine the best properties of existing platforms. The challenges for these platforms lie primarily on the road to large scale integration, as the individual components required for near term application for quantum networking technologies have been demonstrated.

We thank N Sinclair and R Riedinger for helpful conversation. B M thanks NSF GRFP for funding provided via research fellowship. B P acknowledges financial support through a Horizon 2020 Marie Skłodowska-Curie Actions global fellowship (COHESiV, Project No. 840968) from the European Commission. M L acknowledges support from NSF, ONR, DoE, and AFOSR.

¹ Texas A&M University, College Station, TX 77840, United States of America

² PN Lebedev Physical Institute, Moscow 119991, Russia

³ M.V. Lomonosov Moscow State University, Moscow 119992, Russia

⁴ Russian Quantum Center, Moscow Region 143025, Russia

Waveguide QED offers a complementary paradigm to cavity QED for studying and regulating light–matter interaction which forms the cornerstone of state-of-the-art chip-scale photonics. Nanofiber-controlled fluorescence from an evanescently coupled atom was first demonstrated by Kien et al [157]. The radiative behavior of multi-emitter configurations is governed by the relative location of the emitters, allowing more efficient control on photon transport and possible adoption as a prototypical element for quantum information. As quantum emitters, cold atoms have largely led the way in the engineering of strongly integrated atom-waveguide architectures, due to their perfect coherence properties. Enhanced Bragg reflection off a chain of identical atoms trapped in an optical lattice in a waveguide was demonstrated in [158]. An ensemble of emitters interfacing with a waveguide, as shown in figure 22, exhibits a myriad of exotic phenomena such as single-photon super- and sub-radiance [159, 160], nonreciprocal photon transport, and asymmetrical Fano lineshapes. When the lattice periodicity equals an integer multiple of the wavelength, the cooperative emission from the atomic array retains its Lorentzian profile with a linearly scaling decay rate, as has been demonstrated in [159, 161]. By stimulating interaction between photons, a multi-spin cluster can serve as an optical switch or nearly any possible quantum gate. Possibility of transparency due to single-photon transport across differentially detuned two-level emitters has been theoretically demonstrated, without applying any control field [160]. Directional dependence of the emission can entail asymmetric relaxation rates to the left- and right-propagating modes, which significantly modifies the transport. The interaction mediated by an optical fiber wields flexible control on both dispersive and dissipative couplings, level repulsion and attraction, and on sensing capabilities [162]. All these ideas can be contextualized in a variety of experimental models of topical interest such as resonators on a transmission line, cold atoms near a fiber and QDs coupled to plasmonic excitations in a nanowire or photonic crystal waveguides [163, 164]. Among solid-state candidates, some promising ones are epitaxy grown QDs, color centers in diamond and solids like SiC, and rare-earth defects in glasses and crystals. As a versatile platform for photonic-state engineering, SFWM stands out as a unique resource for executing a broad class of quantum phenomena in a fiber-optic format [165, 166].

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Currently, the prime challenge is to develop a universal platform for integrated waveguide devices, which would allow easy scalability for industrial applications. The propagation of nanofiber-guided light through a periodic array of identical emitters has been extensively studied. While these works lay out a propitious roadmap for the novel possibilities with waveguide QED, a majority of them, starting from the demonstration of transparency to sensing of anharmonicity, premise their analyses on loss-free or low-decoherence models. To realize these effects with better precision requires better control on extraneous decoherence and overlap in the spatial modes of incident and scattered waves. Indeed, if one considers current information technologies, the only photons used now are at telecom frequencies, while the majority of trailblazing results are being unveiled in the visible and near-infrared domains, where there are plenty of convenient laser sources and familiar high-quality emitters. The conversion of optical to telecom frequency at the level of single photons, which is interesting for QIP, still poses a challenge. Remarkable progress has been achieved with diamond-based waveguides. No less challenging is optimizing the choice of quantum emitter itself. An obvious trend is to deploy solid-state emitters, but unavoidable decoherence and strong scattering off phonons brings down the quality of these emitters, even at cryogenic temperatures. Nevertheless, the impact of decoherence channels in generic waveguide-QED models has been theoretically studied from rigorous, first-principle considerations [167]. NV color centers in diamond can boost the coherence at cryogenic temperatures but defects intrinsic to nanostructures can be an issue. The problem of inadequate coupling could be overcome to some extent by integrating photonic cavities to waveguides, but cavities are unfortunately bulkier. Previously mostly ignored for their very weak optical transition, rare-earth ions in crystals are showing functionalities via their telecom transitions and possibility of strong enchantment in photonic crystal cavities. Furthermore, quite generally, chiral waveguides provide an entirely different setup for manipulating photon scattering. Therefore, the controllability of chiral characteristics and the feasibility of unidirectional emission merits further investigation. Finally, with regards to quantum-state generation, nonlinear methods like FWM in optical fibers are becoming successful as recent efforts have shown [165, 166].

Although experimental investigations on photon transport in waveguide-integrated setups have picked up speed over the last two decades, it is imperative to make continual upgrades to bridge the chasm between theory and experiment. The subwavelength-sized mode volumes in cavity QED made it possible to reach even ultrastrong atom-photon coupling, however many waveguide-based platforms are still lagging behind in implementing efficient photon–emitter interaction required for fabricating chip-scale optical devices. Interestingly, the cold-atom community is now investigating not only multi-atomic systems coupled to waveguides, but also into possibilities of constructing waveguides from atomic arrays themselves [168]. With diamond-based platforms, several amazing results involving SiV centers, on strong coupling, all-optical switching of photons and realization of quantum gates in all-optical cavities in diamond-made cavity were demonstrated [60]. While color centers in SiC show clear promise in moving to industry-friendly applications, they have a lot of catching up to do in comparison to diamond-based structures. There has been a number of advances in positioning and even fabrication of the nanocrystals themselves, which has created potential for these systems to compete with pure diamond cavities or silicon-carbide cavities [169]. Plasmonic structures recently focused on development of low-loss surface plasmon polaritons as well as growing low-loss plasmonic materials. When implemented in optical fibers, spontaneous FWM provides a vast arsenal of methods and an ample parameter space for engineering photon entanglement in spectral, temporal, spatial and polarization modes. Advanced methods of fiber-dispersion management, on the other hand, may prove instrumental for entanglement-time engineering [166]. As one of the recent trends, FWM with cross-polarized pump and sidebands finds growing use as a powerful resource of quantum entanglement, enabling creation of efficient fiber-optic sources of strongly antibunching heralded single photons [165] and high-brightness entangled photon pairs [166].

Fiber-mediated coherence between emitters is instrumental to the sensing potential of these devices and can also generate long-range inter-emitter entanglement. In order to deftly explore topological phenomena in qubits coupled to fiber waveguides, more technical sophistication based on modern nanofabrication methods is needed to increase the qubit-waveguide coupling.

With the sheer amount of progress being made in waveguide QED, waveguide-integrated circuits and networks are continually expanding the frontiers of research in purely optics-based QC. The Fano-like interference between multiple emission pathways in the photonic interaction with an array of spatially separated emitters makes the photon transport strongly nonreciprocal and sensitive to the spatial separation. In addition, regulation of chiral couplings grants tremendous information processing potential to fiber-integrated multi-emitter devices. The dissipative interaction mediated between the emitters enables one to not merely entangle these emitters but also to explore exceptional point induced phase transition, without resorting to extrinsic gain as is usually the case with directly coupled systems. Finally, optical fields tailored in waveguide and fiber-optic systems lend a vast parameter space, defining the spatial, temporal, spectral, polarization, and spin modes of photons, thus opening new avenues for quantum information science, quantum metrology, and ultrahigh-resolution quantum imaging.

The authors acknowledge the support of The Air Force Office of Scientific Research (Award No. FA9550-20-1-0366), The Robert A Welch Foundation (Grant Nos. A-1943; A-1801), Herman F Heep and Minnie Belle Heep Fellowship, Texas A and M University (X-Grant 497); National Science Foundation (PHY-1820930), Texas A&M College of Science STTR grant, Russian Foundation for Basic Research (Project Nos. 18-29-20031, 19-02-00473), Russian Science Foundation (Project No. 20-12-00088), Ministry of Science and Higher Education of the Russian Federation (Project No. 14.Z50.31.00400).

Kartik Srinivasan

Status

QFC generally refers to the spectral translation of a quantum state of light, such as a single-photon state, between frequency bands. Its role in quantum information science and technology is well-defined in the context of quantum networks (figure 23), where it can enable telecom-wavelength fiber optic links between visible wavelength local quantum systems (e.g. quantum memories). More generally, QFC is needed to make interconnections between quantum systems operating at different wavelengths, for example, to connect a trapped ion quantum processor to a neutral atom ensemble quantum memory. QFC may also have relevance in being able to convert photons to wavelengths for which single-photon detectors have the highest performance, though ever-improving superconducting single-photon detector technology has now made efficient and low-noise detection from the ultraviolet to the near-infrared possible.

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The two main requirements for QFC are high conversion efficiency, so that a large fraction of the input photon flux is frequency converted to the target output frequency, and low added noise, so that the output frequency channel is dominantly composed of light originating from the input source (rather than spurious photons). In the 30+ years since QFC was first discussed explicitly in the literature [170], efficient and low-noise QFC demonstrations have been powered by advances in nonlinear optical technology, in particular based on sum- and difference-frequency generation in quasi-phase-matched nonlinear crystals [171] and four-wave mixing in optical fibers [172], though multi-level atomic systems can also be used to mediate QFC, as has been demonstrated with cold atomic gases [173], for example. QFC with true SPSs has by now been demonstrated many times [174], and in recent years has been used to connect disparate systems such as a cold atomic gas (at 780 nm) and a solid-state crystal (at 606 nm) [175] and to enable entanglement of Rb quantum memories (at 780 nm) across a >20 km fiber optic link [176].

For many such experiments requiring discrete QFC elements, a blueprint for operation has been established. The dispersion of a material creates a phase-mismatch between the fields involved in a nonlinear process and without compensation, limits the maximum achievable conversion efficiency. Materials such as LN combine the ability to realize quasi-phase-matching by periodic poling [171]—a particularly effective approach for overcoming dispersion—with a strong nonlinear coefficient and broadband optical transparency, resulting in near-unity internal conversion efficiency being shown in some cases. Waveguide geometries provide a few centimeter interaction length while retaining bandwidths that are sufficiently wide for a broad range of quantum sources and memories. Low-noise operation typically involves having wide spectral separation between the pump source that mediates frequency conversion (whose power can easily be >10¹³ that of the input quantum light source) and the input signal frequency and target output frequency. Together with appropriate spectral filtering, this limits the extent to which broadband processes (e.g. Raman scattering, parametric fluorescence, and defect-mediated fluorescence) can produce noise that overlaps with the input and output frequency channels, particularly when a long wavelength pump can be selected [178].

Current and future challenges

Advances in science and technology to meet challenges

Integrated photonics is being developed in a wide range of materials of relevance to quantum photonics [180]. This section identifies several important aspects of this technology as it pertains to QFC.

Materials for QFC

Although the maturity of silicon nanophotonics provides strong motivation for its adoption when possible, applications often require functionalities such as gain, broadband optical transparency, and fast, low-loss switching, that are not easy to achieve in silicon. This has motivated research on platforms that have more suitable properties but are still amenable to similar nanofabrication processes. For nonlinear optics, LN remains a preferred choice for second-order processes, and its availability in thin film form offers new opportunities for dispersion control, power reduction, and integration. AlN is another wide-bandgap, second-order nonlinear material available in thin-film form. For third-order nonlinear processes, SiN and Ta₂O₅ offer broadband optical transparency and a nonlinear coefficient that is more than an order of magnitude larger than silica optical fibers, which have been the dominant four-wave mixing platform for decades and have been used in QFC experiments based on the four-wave mixing Bragg scattering process [177]. With an appropriate choice of material composition, III–V materials from the InGaP and AlGaAs families can provide both sufficiently broad optical transparency and a very large optical nonlinearity (both second-order and third-order), while diamond may be a natural choice for third-order QFC applications that involve its color center quantum emitters and/or spins. To that end, we also note that QFC approaches involving multi-level single quantum emitters coupled to nanophotonic elements have also been proposed [181].

Control of nonlinear processes

Nanophotonic geometries provide stronger optical confinement than conventional geometries such as optical fibers or silica planar lightwave circuits. One consequence of this confinement is its impact on dispersion, as the fraction of the field that resides within the waveguide core strongly depends on wavelength and core geometry. As a result, intrinsic material dispersion can often be compensated by precise tailoring of a nanophotonic geometry [182], thereby providing phase-matching that has enabled QFC configurations not easily accessible otherwise. For example, four-wave mixing QFC between 980 and 1550 nm (on-chip efficiency ≈60%) was recently shown in SiN microrings [183] and constituted a wider spectral gap than previous demonstrations in optical fibers; efficient and low-noise visible-to-telecom QFC has also been proposed using similar devices [184]. Geometric dispersion engineering can also be combined with quasi-phase-matching [185]. Moreover, nanophotonics can provide access to other frequency shifting mechanisms, for example based on acousto-optics, that can be used in some scenarios [186].

Low power QFC

A typical pump power for efficient QFC in conventional quasi-phase-matched waveguides is about 100 mW, while in optical fibers, Watt-level powers are often needed. Nanophotonic geometries can reduce such powers, particularly when microresonator geometries are employed, due to the combined effect of confinement and long photon lifetimes. The aforementioned SiN microring QFC [183] achieved high efficiency at the ≈10 mW power level, and reduction to the 1 mW level should be possible through improved cavity performance (higher quality factors) or a more nonlinear material (e.g. a wide-bandgap III–V system). Such powers can easily be accessed by chip-integrated lasers; alternately, it would also allow a single off-chip pump laser to service multiple QFC elements. While a resonant cavity limits the photon conversion bandwidth, the ≈1 GHz bandwidth typical of high quality factor integrated microcavities is adequate for most high-performance quantum emitters, including InAs/GaAs QDs (as used in nanophotonic QFC in [187]).

Understanding and mitigating noise

One important task for nanophotonic QFC platforms is an understanding of added noise sources. While it can be expected that the main noise categories will include Raman scattering, spontaneous parametric processes, and fluorescence, each must be understood and characterized in the context of the material platform and geometry under investigation. Moreover, although a nanophotonic geometry can provide enhancement of the target QFC process, it may also enhance unwanted noise processes. Moving beyond creation of spurious photons, thermorefractive noise may limit the frequency stability of converted photons, which can be of importance when working with narrow linewidth sources.

Integration

One of the most compelling reasons for pursuing nanophotonic QFC is the potential for seamless integration with other photonics technologies, which can simplify the deployment of full QFC systems in applications. Along with combining the QFC element(s) with linear components such as filters and couplers, integration with pump lasers and other quantum photonic elements, such as SPSs and solid-state spins, is feasible, particularly in the context of hybrid photonic platforms that combine the advantageous characteristics of dissimilar materials [4]. Figure 24 gives two examples of nanophotonic QFC systems that can be envisioned based on current technology.

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Concluding remarks

Acknowledgments

Department of Electrical Engineering, Yale University, New Haven, CT 06511, United States of America

QPICs have received growing interests since such platforms offer the stability and integrability towards solid state quantum applications. By encoding quantum information into the optical photons, the QIP, QC and quantum metrology would benefit from the merits of the bosonic carriers, including the high propagation velocity, long propagation distance and infinite-dimensional Hilbert spaces. Single-photon nonlinearity enabled by quantum two-level systems is essential for future quantum information technologies, as they are the building block of quantum photonics logic gates, deterministic SPSs and for coupling distant nodes to form a quantum network.

Microwave photons could be processed by superconducting quantum circuits, where high fidelity quantum operations approaching error-correction thresholds are achieved by the lossless nonlinearity inherent to Josephson effect at cryogenic temperatures [188]. However, at optical frequencies, the absence of the single-photon nonlinearity has been a major roadblock in developing quantum photonic circuits. While the photon–photon interactions required to realize quantum gate can be mediated through light–matter interaction with atomic or atom-like solid-state emitters, their cryogenic temperature requirements greatly reduce the prospects for portable devices and routes to scaling such systems remain challenging [135].

Recent progress in nonlinear optical materials and micro-/nano-resonators has brought single-photon non- linearity employing bulk optical nonlinearities into the realm of possibility [96]. One significant advantage of this approach is its great potential for emitter-free, room temperature quantum photonics applications. In figure 25(a), we illustrate the single-photon nonlinearity in a χ⁽²⁾ cavity, which is intrinsically attributed to the strong single-photon coupling rate g surpassing its dissipation rate κ and thereby is quantified by the figure of merit FOM = g/κ. Figure 25(b) summarizes the coupling rates, dissipation rates as well as the corresponding single-photon nonlinearity FOMs in various integrated χ⁽²⁾ photonics platforms, which are elaborated in [189]. We note that the state-of-the-art g/κ is approximately 0.01 and remains two orders of magnitudes smaller than unity for practical applications.

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Significant engineering efforts are required to maximize the nonlinear coupling strength g while minimizing the cavity loss $\kappa$ simultaneously and thereby advance the directions and applications laid out in the previous section via single-photon nonlinearity. Theoretically, in a χ⁽²⁾ cavity, $g \propto \chi _{{\text{eff}}}^{\left( 2 \right)}\gamma /V$ and $\kappa \propto 1/Q$ give the single-photon nonlinearity FOM $\propto \chi _{{\text{eff}}}^{\left( 2 \right)}\gamma Q/V$ and, where $\chi _{{\text{eff}}}^{\left( 2 \right)}$, γ, V, and Q denote the effective nonlinearity, spatial mode overlap, mode volume and optical quality factor, respectively. While individual parameter seems readily optimized in different platforms, several technological challenges should be tackled to ensure an ultimate optimization of FOM in one single platform as outlined below:

Trade-off between Q and V

Phase matching for integrated cavities

To circumvent the aforementioned challenges, many advances would greatly benefit the future of single-photon nonlinearity in integrated quantum photonics employing bulk optical χ⁽²⁾ nonlinearity for potential deployment. Some advances include the following:

Material platforms with ultralow-loss

Novel photonic structures

Although recent advances on the ultralow-loss demonstration of thin-film LN and AlGaAs integrated circuits along with their significant χ⁽²⁾ nonlinearities show very encouraging performance, research on the single-photon nonlinearity in integrated quantum photonics employing bulk optical nonlinearities remains at its early stages and experimental implementation has yet to be demonstrated. Further breakthroughs on high Q/V integrated resonator fabrication and strong χ⁽²⁾ coupled device design are required to reach the single-photon nonlinear regime, and pave the way for the emitter free, room-temperature quantum photonic applications.

We acknowledge financial support from Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Grant No. DE-SC0019406.

Department of Applied Physics, Ginzton Lab, Stanford University, Stanford, CA 94305, United States of America

The ability to control quantum coherence and entanglement in several physical platforms has now reached the level where significant industrial resources are being applied to realize the promises of large-scale QIP. One such platform consists of superconducting circuits operating at microwave frequencies. Microwave frequency photons are used to store, process, and control the internal quantum dynamics of these systems. The most striking recent manifestation is the result achieved by Google in 2019 on a processor consisting of 53 microwave-frequency qubits [82]. Though this experiment demonstrated that a quantum processor can perform tasks beyond the reach of classical computing technology, it is nonetheless possible that much larger-scale systems consisting of many more qubits will need to be realized before 'useful' quantum computing algorithms can be routinely used to solve problems of real scientific, industrial, and commercial interest. One approach to facilitate scaling is to implement quantum transducers that can act as transparent interfaces between distant microwave-frequency nodes in a quantum data-center. The advantage of such an approach is that it would enable increased modularity in the system design, enable implementation of specialized (and possibly heterogeneous) subunits that can perform certain tasks more efficiently, and enable larger scales by distributing computational tasks across many cryogenic systems which can be operated independently. A natural approach to this problem is to realize a microwave-to-optical converter that efficiently interconverts between microwave and optical photons. The most important characteristic of a microwave-to-optical transducer is the rate of entanglement generation between optical and microwave photons that is possible given the constraints on dissipated power and other deleterious effects caused by absorption of light. Other important factors are the bandwidth, efficiency, whether the converter can support heralded operation, and the ease at which it may be scaled up to more channels. Fundamentally, a nonlinear process must occur to change the photon frequency. At this stage, the hardware remains the primary challenge and is the focus of this roadmap. We consider here the approaches based on the direct EO conversion, and approaches that use an optomechanical resonator as an intermediary. There are also promising approaches based on rare-earth dopants or other solid-state emitters, which we will not discuss here due to lack of space, but note that they share many of the same implementation challenges [192].

Figures of merit

Electro-optic conversion

Optomechanical conversion

Controlling coupling and noise

We discussed the current state of the art EO converters, which use either the direct EO effect in a material with a high EO coefficient such as LN, or use an indirect piezo-optomechanical approach. Achieving highly efficient conversion remains a daunting task requiring optimization and ultra-high performance from every part of a whole heterogeneous system. With several paths forward on all remaining technical challenges, we expect transducers to become reality in the next decade and to enable a variety of new and exciting applications in quantum computing, communications, and sensing as well as forming part of the technological bedrock of an emerging quantum internet.

Stephan Steinhauer, Ali W Elshaari and Val Zwiller

Status

Current and future challenges

Ongoing research and developments efforts aim at further improvements of the SNSPD performance metrics at the single-device level. SNSPD devices with enhanced properties are needed as several QIP schemes place stringent requirements on certain detector parameters, in particular detection efficiency and maximum count rate. Photon number resolution (PNR) is another important capability required for many quantum protocols and linear optical quantum computing [206], which is typically not offered by SNSPDs. Alternatively, transition-edge detectors would provide the possibility for PNR, but they often need to be operated at low temperatures in the 100 mK range and are linked with disadvantages of slow reset times in the microsecond range and limited timing resolution. Significant progress has been achieved in the development of SNSPDs with pseudo PNR, relying on spatial multiplexing in arrays of superconducting nanowires [207].

Figure 26 shows different device concepts for single-detector, multi-detector and cavity-enhanced SNSPDs integrated with photonic circuits, highlighting their advantages and shortcomings. To achieve GHz detection rates, it is required to minimize the reset time of the detectors to the sub-nanosecond range. Although decreasing the device length reduces the kinetic inductance and hence the detection pulse decay time constant, this approach places limitations on the on-chip detection efficiency due to reduced waveguide-detector interaction length. This challenge has been successfully addressed by integrating SNSPDs with 1D and 2D photonic bandgap cavities, boosting the on-chip detection efficiency for short nanowires. However, it remains a major challenge to simultaneously optimize several key detection parameters and combine them with (pseudo) PNR capabilities.

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Moreover, scalability and yield, i.e. the ability to reproducibly fabricate waveguide-integrated detectors with tight control over their properties such as critical current, on-chip detection efficiency, and timing resolution, are at the forefront of current challenges. Additionally, realizing radically up-scaled systems with many independently addressed waveguide-integrated detectors can pose challenges on the readout scheme. Although a free-space coupled kilo-pixel SNSPD array suitable for imaging systems was recently realized using a row-column multiplexing architecture [208], demonstrating even larger systems in conjunction with complex networks of integrated quantum photonic devices will require sophisticated interfacing and multiplexing solutions.

Advances in science and technology to meet challenges

Concluding remarks

Acknowledgments

Sandia National Labs, Albuquerque, NM, United States of America

Detection at extremely low-light levels is of fundamental importance for imaging and remote sensing applications and lies at the heart of quantum information systems and interconnects. SPDs are a key building block device of quantum photonics, which integrates quantum optical circuits onto a densely integrated chip-scale platform that leverages advanced Si-CMOS processing and heterogenous integration.

Commercially available SPDs are available in a number of technologies. The highest performance detectors are based on superconducting nanowires, providing high single photon detection efficiency and low dark counts, with the drawback of required cooling below 4 K, making them impractical for many applications. An alternative technology is single photon APDs (SPAD) utilizing charge multiplication to convert a single photogenerated carrier into a detectable current pulse. Sillicon based SPADs provide high efficiencies in the visible and near infrared wavelengths, while InGaAs versions provide operation out to telecom wavelengths. The ability to operate near room temperature increases the appeal of this technology. Implementing this technology in a scalable CMOS fabricated quantum integrated photonic platform is desirable to realize deployable, low power quantum devices. One path towards this integration is to utilize epitaxial growth of Ge on Si in a separate absorption and charge multiplication APD (SACM-PD). This device, demonstrated near room temperature, takes advantage of the low noise avalanche gain provided by intrinsic silicon, combined with narrow band absorption of germanium [212, 213]. Figure 27(a) shows a schematic and fabricated cross-section of the waveguide-coupled Ge absorption layer and lateral Si multiplication APD device. These SPDs work in the telecom bands and operate with moderate cooling near room-temperature and can be deployed in QKD chip-based transceivers that do not rely on high SPD efficiency [214]. Figure 27(b) shows the impact of temperature and Geiger mode gate duration on dark counts and illustrates the need for significant reduction in dark count rates. Thermal generation in semiconductor photodetection is intrinsic due to the bandgap of the photo-absorbing material and can be mitigated through extreme volume reduction of the absorber material to reduce the impact of bulk and surface defects and by cooling of the device. The single photon detection efficiency and the dark count rate are complex functions of the Geiger mode operation of the device and depend critically on the gate duration, repetition rate, over bias, temperature, and device size. For advanced quantum interconnect applications, dramatic improvement in the performance of uncooled integrated SPAD's is required due to the preciousness of each photon.

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Moreover, non-cryogenically cooled SPDs with selected wavelength absorbers can be used in a host of applications; such as to extend the range of LIDAR systems, improve scintillation for radiation detection, reduce power consumption in focal-plane array imagers, and for quantum sensing for chip-based atomic sensors. These semiconductor-based devices are compatible with advanced CMOS manufacturing processes and with advances in heterogenous integration can be integrated into complex photonic circuits. Further research and development on integrated SPAD devices is needed to reach the full potential of these devices for quantum interconnects.

Single-photon detectors based on APDs (SPAD) work by amplifying a weak photogenerated current from a single absorption of a photon into a detectable signal while supressing dark detection events due to thermal or defect driven processes in the device. These two processes seem to be in opposition, indeed the high amplified device currents needed can create localized heat sources and emit out of band photons which can influence dark counts in nearby detectors. However, by reducing the active volume of the narrow bandgap absorbing material and reducing defect density at interfaces we can mitigate thermal generation effects that contribute to dark counts in these devices. Continued advances in semiconductor processing and integrated control circuits can be used to reduce these effects.

A major challenge in semiconductor SPDs is to reduce spurious dark counts while maintaining high quantum efficiency. Dark count rates can be manipulated with temperature but other methods, specifically fabrication, exist to reduce these noise sources. In selectively grown epitaxial structures on Si, defects exist at interfaces due to lattice mismatch resulting in strain which can act as traps and release carriers in strong fields. Graded strain relief layers can be used to reduce the interfacial defects. Furthermore, by reducing the selective growth interface area where defects from the lattice mismatch occur, the crystalline quality of the selectively grown material is greatly improved through aspect ratio trapping, and defect areal density is reduced. Figure 27(c) illustrates the modified selective epitaxial template for aspect ratio trapping growth of Ge. Another device technique to reduce dark counts is by operating the SPAD in gated Geiger mode. This high-speed Geiger mode gating acts as a system level trick to reduce the influence of dark counts by reducing the probability of triggering a dark event in a small gate time window which is similar to lock-in techniques. However, this method requires that the arrival of the single photon signal to be in a synchronous timing window for detection. Gated operation gives rise to capacitive feed-thru response and various circuit subtraction methods can be used to reduce the triggering threshold [215]. Furthermore, careful consideration and design of the location of high electric field regions within the device can be tailored to avoid high defect surfaces using doping, symmetrically placed electrodes, strain engineering and other semiconductor processes. Similarly, photonic design principles can be used to improve light trapping in the waveguide coupled structure and to remove parasitic absorption that does not lead to viable photogeneration.

Low-defect selective epitaxial growth of Ge or related materials on Si by UHV-CVD processes with in-situ doping in compact templates would be a significant scientific advance that would benefit semiconductor-based SPDs. Novel photonic light trapping structures integrated into SACM-APD devices that resonantly confine light to subwavelength volumes offer potentially efficient single photon detection with moderately cooled devices. Furthermore, integrated fast electronic gating and signal analysis or hybrid APD coherent detection schemes can be used to improve moderately cooled SPD performance. One key advantage for the separate absorber charge multiplication APD design is the flexibility to change wavelength absorption band by changing the absorber material but retaining the advantages of the Si multiplication. High confinement dielectric resonant absorber designs allow for compact device structures that result in lower bulk thermal generation (see figure 28). Recently, advances in selective epitaxial growth of strained Ge_1−x Sn_x alloys have led to a new high-refractive-index semiconductor alloy with a tuneable direct bandgap for varying Sn concentration (x = 5%–20%) [216]. This allows for strong absorption in the short-wave infrared (SWIR) spectral range with tuning between wavelengths in the range of 2–2.5 µm while maintaining CMOS compatible processing. In the SWIR band, Si remains transparent but with improved free-carrier dispersion effect for active device modulation and a reduction in TPA allowing for interesting possibilities for non-linear optical phenomena on-chip. Ge_1−x Sn_x single photon SACM APD's would allow for the building of a new complete quantum photonics platform with potentially new quantum and classical applications [217–219].

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SNSPDs with background limited performance have been demonstrated with the major drawback that they need to operate at cryogenic temperatures near 4 K which may not be practical for some applications [220]. Recent developments in semiconductor based SPDs based on compact Ge on Si separate charge absorption and multiplication region APD's present opportunities for large scale integration and improved performance through fabrication advances and designs in applications that are non-cryogenically cooled. Remember that the human-eye is a few-photon visible light sensor that operates above room-temperature!

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy's National Nuclear Security Administration under Contract DE-NA0003525.

This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

John Chiaverini¹,² and Karan K Mehta³

Status

Atomic ions held in electromagnetic traps and manipulated with lasers and/or radio-frequency and microwave fields form one of the most promising physical implementations of QIP [11]. Current systems employed in industry, academia, and national laboratories can precisely manipulate up to a few tens of ions in 1D arrays with sufficient control to perform basic quantum algorithms. However, optical systems currently used for trapped-ion control, mainly based on bulk optics, are susceptible to substantial noise and drift that can introduce errors even in few-qubit operations. Furthermore, they are challenging to make extensible as required to surpass noisy intermediate-scale quantum (NISQ)-era scales [221] and thereby enable practically relevant quantum computation.

An approach instead relying on photonics tightly integrated within ion trap chips offers a path to addressing these challenges. In this architecture, as illustrated in figure 29, the multiple visible/UV wavelengths required for ion control and readout are routed on-chip and emitted, via diffractive elements, toward ions held in surface electrode traps typically 50–100 µm above the electrode surfaces. Single-photon detectors integrated in such a platform would allow for qubit state readout in largescale arrays via site-specific fluorescence collection. Additionally, waveguide splitting and appropriate active devices would allow frequency, phase, and amplitude control of optical fields as required for parallel modulation of a number of channels in excess of the number of optical inputs to the device.

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Experiments to date have demonstrated the core addressing element of this architecture [222], at all wavelengths relevant to particular species [15], as well as in low-error multi-qubit operations [10]. Realization of the full set of components and functions required for optical control and readout of precise, large-scale trapped ion systems for quantum computation, simulation, and precision measurement motivates basic research and development along multiple lines in the years ahead.

Current and future challenges

Advances in science and technology to meet challenges

Concluding remarks

Acknowledgments

Jacquiline Romero

Status

Qudits [231]—the d-level version of the more ubiquitous two-level qubit—should figure greatly in future quantum technologies, whether they be for communication, sensing, or computation. The most compelling reason is that quantum systems are naturally high-dimensional. The restriction to qubits is not necessary, particularly when engineering coupled systems together is difficult and qudit entanglement is physically possible. Qudits have the potential to outperform their qubit counterparts by providing access to a larger state space for storing and processing quantum information. Integrating qudit systems—like those that exploit multiple degrees of freedom—offers more favourable scaling than multi-particle qubit approaches because detection rate significantly decreases as the number of entangled particles becomes larger. Qudit advantages have been shown for QC and quantum computation, e.g. qudits lead to enhanced robustness against eavesdropping and simplified gates. More importantly, qudit entanglement has been shown to overcome noise in entanglement distribution, which is important for any future QC network [232].

It is well known that a photon possesses several properties that naturally accommodate a qudit description, e.g. path, frequency, time-bins, photon number, and transverse spatial mode such as those associated with orbital angular momentum (OAM). Long room-temperature coherence times, ease of transmission via free space or optical fibre, and availability of efficient detectors also make photonic platforms excellent for implementing quantum technologies based on qudits.

Photonic qudits on chip is a nascent field but there have been some notable results in recent times. The most mature photonic qudit on chip platform uses path encoding: in [6] Wang et al demonstrated 15 × 15 dimensional entanglement using a silicon photonic device that integrated photon-pair sources, multimode interferometers, phase-shifters, beamsplitters, waveguide crossers, and grating couplers; in [34] Llewellyn et al demonstrated quantum teleportation between two silicon chips. Using time and frequency encodings (figure 30), both Imany et al [233] and Kues et al [234] demonstrated two-qudit gates acting on photons generated via SFWM in a microring resonator. Exploiting the transverse spatial modes, an on-chip source of polarisation and OAM modes have been demonstrated on a silicon platform, and quantum interference has been demonstrated using photons generated from SPDC and SiN waveguides that act as mode multiplexer and mode beamsplitter [235] (figure 31).

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Current and future challenges

Advances in science and technology to meet challenges

Concluding remarks

Acknowledgments

School of Electrical and Computer Engineering and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, United States of America

Quantum frequency combs are the single- or few-photon analog of classical frequency combs. As one might presume, these states populate a superposition of modes that are equidistant from one another in frequency. What makes them particularly attractive is that they can support many temporal and frequency modes (figure 32); high dimensionality and hyperentanglement can potentially offer a large quantum resource over just a few photons. Quantum frequency combs were first observed in OPOs pumped below threshold. More recent interest in the field was spurred by the generation of two-photon quantum frequency combs in CMOS-compatible optical microresonators [234, 240]. Owing to their compact geometry, these sources support free spectral ranges in the 10 s of GHz—a range well suited to commercial telecom equipment. Recent accomplishments [68] include characterization of high-dimensional frequency-bin entanglement, single-photon two qudit gates, generation of four-party 32-dimensional Greenberger–Horne–Zeilinger states, and nonlocal delay metrology featuring picosecond-scale resolution with potential relevance to the synchronization of quantum networks [241].

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Progress in the field also extends to the emergence of a paradigm for QIP with comb-like states. Like any platform, one needs to access individual modes to apply prescribed phase shifts, as well as mix a combination of modes in any desired ratio. The former is readily accomplished with programmable filter banks or Fourier transform pulse shapers. The latter, on the other hand, poses a real challenge as there is no off-the-shelf component to mix frequency modes in an arbitrary manner. To overcome this limitation, a team at Oak Ridge National Laboratory devised a protocol capable of arbitrary spectral transformations using EOMs and Fourier transform pulse shapers [242]. This concatenation, called a quantum frequency processor or QFP for short, was used in a series of demonstrations over the last couple of years, culminating in completion of the gate set for frequency [68].

This progress in realizing arbitrary spectral transformations is perhaps most relevant to the development of quantum interconnects, which would benefit from the ability to implement high-dimensional gates, work with spectrally multiplexed quantum channels, and carry out in-band QFC.

Outside of photon pair sources, experiments to date have relied on off-the-shelf telecommunications equipment to manipulate and retrieve quantum information. However, such experiments have some important limits. One drawback to working with discrete components is that they have high insertion losses (4 dB for EOMs and 5 dB for pulse shapers). Reducing these losses is critical for scalable QIP and deployment in quantum networks.

Another limit is that adjacent modes must be separated by at least 20 GHz—set by the resolution of commercial pulse shapers—in order to avoid crosstalk. Consequently, if one wants to efficiently mix even just adjacent modes, EOMs need to be driven with at least a 20 GHz radiofrequency (RF) drive tone. However, to connect more distant modes, or implement high-dimensional quantum gates using a QFP, one needs access to not just a 20 GHz tone but also to higher RF harmonics. For example, to permit the full range of 2D quantum operations with both high fidelity (>0.9999) and high success probability (>0.95) using just two modulators and a pulse shaper, the RF drive needs to include at least two harmonics. Similar behavior holds for higher dimensions as well. This points to a unique advantage of the QFP protocol—gate complexity can be scaled without any increase to the number of physical elements! This interplay between the modulator bandwidth (BW_RF) and the fundamental mode separation (FSR) suggests a rough gauge of operation complexity. To first order, the ratio BW_RF/FSR corresponds to the highest dimensional gate set one can synthesize using a three-element QFP. Thus, even with a generous RF bandwidth of 60 GHz, one is limited to just 3D gates owing to the 20 GHz pulse shaper resolution.

For these reasons, realizing the full potential of QIP in the frequency domain will require the migration of functionality to an integrated optical platform. In addition to a reduction in optical loss, integrated photonics will enable more complex operations, either by increasing the number of RF harmonics accessible to the system or by permitting realization of QFPs that comprise concatenations of additional pulse shaper and modulator elements.

Quantum comb sources have benefited from advances in the development of microresonator-based (classical) comb sources. While further refinements, like reducing the comb FSR, are desirable, there is a greater need for tools to manipulate frequency-encoded quantum information on chip. This includes pulse shapers for channel-by-channel phase control and EOMs for frequency mixing (figure 33).

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Pulse shapers can be realized using banks of tunable ring resonators [243] and are not tied to any one material system. Low waveguide propagation loss (<1 dB cm⁻¹) has been reported in a variety of platforms at both academic facilities [74] and at commercial foundries [244]. These developments, coupled with astute design choices, have made it possible to realize sub-GHz filters with minimal drop loss [244]; such elements will enable more closely spaced frequency modes.

On-chip phase modulators compatible with low loss and large-scale photonic integration have traditionally been problematic, but recent research provides new possibilities. Especially notable are developments with TFLN, which has a native EO efficient. By relying on the Pockels effect rather than on free carrier dispersion or some other intrinsically lossy mechanism, devices capable of high-speed operation (>100 GHz) and low propagation loss (0.2 dB cm⁻¹) can be realized [74]. While the headline numbers are impressive, it is important to recognize that average loss alone does not tell the full story. A better prism through which to view modulator performance is the voltage-loss product expressed in VdB. Quite simply this is the loss incurred when the modulator is scaled to support a half-wave voltage of 1 V. TFLN leads the pack (αV_π L = 0.5 VdB), but indium phosphide (0.9 VdB) [245], as well as more exotic approaches like silicon-organic hybrids (1.0 VdB) [246], are not far behind and have advantages in terms of platform maturity and economies of scale.

At the device level, progress in coupled-cavity modulators [246] or so-called 'photonic molecules' offers a complement to the QFP protocol. These devices comprise two evanescently coupled optical microresonators and, owing to mode hybridization, can scatter an input light field between two, and only two, closely separated spectral modes—an operation potentially equivalent to a frequency qubit rotation.

It is notable that frequency bin quantum photonics has synergies with fields that are the subject of significant research and development interest—Kerr microcombs, RF photonics, and high-performance computing. Quantum frequency combs, like their classical counterparts, can be generated in nonlinear microresonators with low anomalous group velocity dispersion. Scalable production of these sources would make this platform readily accessible to the wider research community. Similarly, progress in high-performance computing and wideband communications hinges on the development of high-speed, low-loss optical switches, which differ from low-loss phase modulators by only a scaling of the device length. While frequency encoding has some catch up to do, the natural advantages of this degree of freedom—stability over standard optical fiber, compatibility with telecom infrastructure, and support for multilevel quantum information—coupled with recent developments in integrated photonics, point to a bright future in the development of practical quantum networks.

The authors acknowledge funding from the National Science Foundation (2034019-ECCS, 1839191-ECCS). N B Lingaraju acknowledges support from a QISE-NET Triplet Award (NSF 1747426-DMR).

Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, QLD 4111, Australia

CV quantum technologies encode information in specific states of the electromagnetic field quadrature operator $\hat q = \left( {{{\hat a}^\dagger }{e^{i\theta }} + \hat a{e^{ - i\theta }}} \right)/\sqrt 2 \,$ whose spectrum has continuous values. This approach offers several advantages compared to polarization and photon number encoding, both with a discrete set of eigenvalues, but is more susceptible to losses. Specifically, the generation of large entangled states and high efficiency detection are open problems and technological challenges for discrete variable (DV) systems. In contrast, quadrature entanglement and squeezing can be generated deterministically, and homodyne detectors (HD) can measure quadrature with efficiency greater than 99%.

Two-dimensional cluster states, which are necessary universal resource for CV computation, have been demonstrated in experiments over several thousands of nodes [247, 248], highlighting the scaling potential of the CV approach especially for MBQC (see figure 34). Furthermore, proposals based on the Gottesman–Kitaev–Preskill (GKP) state encoding [249] recently established a fault tolerance threshold for CV-MBQC. But while a basic computation of ∼100 steps has been demonstrated with 1D cluster [250], the implementation of non-Gaussian resources, which is necessary for universal quantum computation, is still an open problem.

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LN is one of the most widely used materials in photonics. This is because of its wide transparency window (400 nm–5 μm), high second order nonlinearity (d₃₃ = 25 pm V⁻¹ at 1550 nm), and large EO coefficient, which enables fast amplitude and phase modulation. These properties are essential for the realization of a MBQC platform and have been recently demonstrated in a single integrated device where CV squeezing and entanglement was generated, manipulated, and measured [251].

While the experiments in [251] used in-diffused LN waveguide, which are 6–10 μm wide and have a low index contrast, LN-on-insulator (LNOI) waveguides offer scaling properties similar to silicon photonics, but with the cited benefits of LN [252]. Propagation losses as low as 2.7 dB m⁻¹ [252], ultra-fast amplitude modulation, and single pass SHG efficiency more than an order of magnitude higher than their diffused counterparts [252]. So far, uses of LNOI waveguide for quantum photonics have been limited to generation of single photons [252].

The realization of a universal CV-MBQC machine requires technological innovation for the LNOI platform and theoretical advances for the efficient generation of non-Gaussian resources. The error correction threshold for CV 2D cluster based on GKP encoding requires ∼15–17 dB of squeezing, independent on the level of anti-squeezing [253]. This value caps the maximum amount of total loss tolerable in a given circuit to a few percent and includes both propagation and coupling losses in addition to detection efficiency. To date the largest level of squeezing reported is 15 dB, obtained from a semi-monolithic OPO operating in the continuous-wave regime [254].

On-chip generation of squeezed vacuum is currently limited to 6 dB from a ridge waveguides in ZnO-doped LN with a 5 × 6 μm cross section in a single-pass configuration [255]. Broadband single-pass sources are more suited for time-multiplexed 2D cluster states since they enable shorter temporal modes thereby increasing the size of the cluster state for a given time window resulting in a larger computational power. The strong nonlinearity and low losses of LNOI waveguides can provide a crucial advantage over other material platforms [252].

A time multiplexed MBQC is characterized by two main timescales: a short time scale which separates two neighbouring nodes of the cluster, and a long one which set the qubit width of the computation [247, 248]. While a fully integrated approach offers clear advantages (see figure 35), it is possible that CV-MBQC machines will use off-chip delays to increase their computational power and that high efficiency in/out coupling photonic structure will be necessary in order to perform within the fault tolerant threshold.

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Large-scale cluster states and Gaussian operations are not enough for universal quantum computation. Non-Gaussian states, operations or measurements must be included. Utilising GKP encoding is optimal for universality and error correction, but experimentally they are yet to be realised with photonics. For a large-scale system, a high rate of GKP states is required, which remains one of the main fundamental challenges for the realization of a MBQC universal machine.

Recently, spurred by advances in the commercial availability of up to 6'' wafers, the thin film LNOI platform has gained significant interest, with demonstrated low-loss ridge waveguides and small bending radii ($<$100 μm), ultrafast light manipulation, and large nonlinearity, highlighting its potential for scalable quantum technologies in communication, metrology and computation.

With propagation losses as low as 2.7 dB m⁻¹ at 1550 nm and measured nonlinear conversion efficiency of 4600% W⁻¹cm⁻², a periodically poled LNOI waveguide (ppLNOI) can theoretically reach the 15 dB squeezing threshold for fault-tolerance if pumped with ∼130 mW of power in 15 mm long devices. So far ppLNOI waveguides have underperformed in terms of propagation losses when compared to the 2.7 dB m⁻¹ mark, and improvements in the fabrication process are necessary.

The low loss threshold of CV quantum computation requires the integration with high efficiency detectors. Integrated superconducting SPD on LNOI have been recently demonstrated [81] and while the 46% efficiency is not the state of the art, this is an important result. High efficiency photodiodes for HD already exist off chip, an integrated version is yet to be demonstrated. Designs for coupling structures such as grating couplers, tapers, and mode converters have been proposed showing theoretical efficiencies near 80%, however experimental realisations typically half that are still far from the few percent tolerable losses. As such work is still required to further reduce these losses, possibly with the use of inverse design tools and improved fabrication processes.

The efficient generation of a GKP state is the main theoretical challenge for the implementation of a full scale, error corrected universal CV quantum computer. This state is a coherent superposition of a comb quadrature eigenstates that could be generated from optical Schrödinger cat state strongly coupled to a qubit system. No experimental generation of GKP states using photonics has been reported so far. Theoretical proposals based on PNR detectors, squeezed states and linear optical circuits [253] offering an approximate, non-deterministic, heralded path for experimentalists to follow.

The development of the LNOI photonic platform with low propagation losses, large nonlinearity, and ultrafast EO reconfigurability embed several key properties necessary for MBQC. This technology, together with the recent generation of large CV cluster states and theoretical progress for fault tolerant computation hold great potential for the realization of a photonic universal quantum computer. While a LN device has demonstrated the generation, manipulation and detection of CV quantum states, future technological development will focus on the integration of efficient homodyne and SPDs, and low loss delay lines.

Theoretical progress is still needed for the efficient generation of non-Gaussian resources necessary for universal quantum computation. While here we focused on GKP state encoding because it is the one used for the derivation of the fault-tolerance threshold, other proposals to solve the encoding and error correction problem may arise in the future.

This work was supported financially by the Australian Research Council Centres of Excellence Scheme Number CE170100012. M L was supported by the Australian Research Council Future Fellowship (FT180100055).

CNRS, Sorbonne University, Paris, France

Quantum cryptography encompasses primitives that use the properties of quantum mechanics to offer new cryptographic services or provide security advantages with respect to their classical counterparts. It is part of the broader field of QC, which includes all technologies and applications involving the transfer of quantum states between distant locations. QC implementations typically use photons as carriers of information and optical fiber or free space (including satellite) links as communication channels. This makes integrated photonics a key player in the development of these systems, where it can facilitate scalability, reproducibility, interconnectivity and reliability, as well as a reduction in price and physical footprint [256], speeding up the adoption of these technologies at the user level in emerging global-scale QC infrastructures.

QKD [257] is perhaps the most well-known application of quantum cryptography and commercial products are already available. It allows the exchange of a private secret key between two trusted parties over an untrusted quantum channel provided that the parties have access to an authenticated classical channel and true random number sources. The main advantage of QKD with respect to classical alternatives like post-quantum cryptography is that the security does not rely on the computational resources of the attacker, but on the faithfulness of the implementation with respect to the model used in the security proof of the protocol. QKD offers information-theoretic, long-term security, making it an application of great interest in many sectors (medicine, finance, government, defence…) where these properties are essential.

Quantum random number generation (QRNG) is very commonly associated with cryptography, since it uses entropy sources based on the laws of quantum mechanics to generate true random values, which is required for cryptography, including QKD, but is also useful for other purposes. Commercial QRNG products are already available, some of them based on PICs. Other interesting quantum cryptographic primitives include secret sharing, digital signatures, commitment schemes, secure multiparty computation (oblivious transfer, coin flipping) and position-based cryptography. These protocols can involve different assumptions in terms of trust between the users, levels of security and particular requirements at the system level, and offer a wide range of advanced functionalities useful for applications in QC networks. Here, we focus mostly on the challenges on the way to the use of integrated photonics in QKD since these cover the main requirements for the other quantum cryptographic protocols as well.

QC primitives and QKD in particular become interesting when the quantum states can be distributed at relatively high rates and over long distances. On the quest for high-performance QKD systems, a great number of protocols have been successfully implemented [257], mostly in laboratory or field experiments, and more rarely as commercial products, but many improvements need to be made before considering them a mature market (see figure 36 for a general forecast). A major family of protocols are DV ones, where typically coherent states generated by lasers are attenuated and then manipulated in some degree of freedom (polarization, phase, time) before being detected by single-photon detectors. In CV QKD systems, the coherent states are modulated in phase-space and detected by coherent detectors, where the quantum states are mixed with a local oscillator (generated by a laser at the receiver in most modern implementations). While in such systems the receiver needs to be trusted, measurement device independent (MDI) and twin field QKD allow for a third untrusted party to perform the measurements. Fully device independent QKD uses Bell nonlocality to remove trust assumptions from all devices but imposes stringent constraints that cannot be satisfied by currently available technology.

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System demonstrations involving photonic integrated components have been performed for DV [258], CV [259] and MDI QKD [260, 261], based mostly on the Si platform but InP has also been used in some cases. These are essentially proof-of-principle experiments, and a major challenge for these systems is to reach the performance of QKD implementations based on bulk components. To increase the level of integration, it will be necessary to address important challenges that remain on the single-photon detection side and on the operation with multiple polarizations and time delays. Furthermore, in general, a particular photonic integration platform may not be optimal for all of the required components in the system. Advancing towards heterogeneous integration [262] is therefore a crucial challenge, and will also be of great importance for ultimately integrating also the electronic functionalities of the system needed for signal control and data processing. Functionalities linked to network architectures (synchronization, multiplexing, routing) should also be considered.

Since classical signal amplification techniques are detrimental for quantum signals, the range achieved by QKD and more generally by QC systems is ultimately limited by the inherent exponential loss suffered by light in optical fibers. For QKD, this limits the distance over which secret key generation can be performed to a few hundred kilometers, with a strong trade-off with respect to the achievable rate. Ideally, quantum repeaters, which involve quantum memories, can be used for extending the distance. Research efforts are underway toward on-chip quantum memories [263] but several challenges will need to be addressed for such components to be sufficiently mature for use within advanced quantum cryptographic systems. Such systems also rely, for instance, on entangled-photon generation and frequency conversion, where photonic integration has considerably advanced. While developments in quantum repeaters are in process, trusted nodes can be used to extend the range, but for intercontinental distances a more interesting approach is to use satellite communications, where free-space attenuation is quadratic with the distance. Although free-space QKD using Si integrated components has shown promising results [264], to prepare the ground for satellite-based demonstrations it will be necessary to advance towards space qualification of such systems, including their photonic integrated components.

Telecom C-band and O-band are the most common wavelengths of choice in optical fiber communications. Free-space communications can use a broader range, but the current trend is to use telecom wavelengths for compatibility. This creates a lot of synergies with classical communications, in particular for CV-QKD which shares many elements with coherent transceivers, for which implementation agreements from the Optical Internetworking Forum (e.g. TROSA) offer an industry standard. Current devices allow bandwidths of several GHz in the size of a coin suitable for high-rate classical communications, but desirable improvements for quantum systems include higher detection efficiency and narrower laser linewidths.

Efficient detection of single photons at telecom wavelengths is more problematic than coherent detection [265] and it typically requires cooling, which reduces the advantage of integration. An interesting solution in this case is to use integrated transmitters and bulk receivers, which is practical for MDI-QKD protocols as was already shown [260, 261]. Preparation of the quantum states in phase-space is straightforward (using phase, amplitude and IQ modulators) [259], but polarization and time operations can also be performed using custom systems [258, 259].

The interest in significant advances in heterogeneous (or hybrid) integration spans all quantum technologies. Of particular interest for quantum cryptography is wafer-scale SOI, typically interesting for telecommunication wavelengths, Si photonics matched with polymer wave guiding offering advantages in terms of manufacturability, III–V (InP and GaAs) platforms for integrating active sources, and substrates like SiC, which may be interesting for quantum repeaters. It is clear, however, that for these technologies to become relevant for advanced quantum cryptographic system implementations, important developments at the component level are necessary.

Quantum cryptography is a diverse field with a broad range of potential applications. Some applications like QRNG and QKD are already targeting large markets, while other protocols could greatly benefit a niche public before becoming mainstream. The nature of the protocols gives a lot of predominance to the system level of the implementation, making it interesting to provide flexible systems that can operate multiple protocols or configurations with the same hardware. The potential benefits of integrated photonics are extensive as it enables more functionalities to become available as building blocks for different technologies allowing for the design of reliable custom subsystems that can be part of quantum cryptographic systems. Improvements on heterogeneous integration of multiple platforms and packaging (including particular cases such as space qualification) will continue to expand the presence of integrated photonic devices in QC systems, driving their scalable deployment in global network infrastructures.

The authors acknowledge funding from the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement No. 820466 (CiViQ).

Brigham Young University, Provo, UT, United States of America

Machine learning algorithms can automatically learn patterns within a dataset, even in the absence of a physical model. In contrast to most early targets for machine learning, Maxwell equations are well-known with robust numerical techniques successfully developed and commercialized. Machine learning has become valuable in photonics primarily owing to its reduced computational cost. Traditional full-wave techniques, such as finite-difference time domain, finite element method, and others, solve Maxwell’s equations directly, but become costly with larger systems. This problem is compounded for design problems, in which a geometry is sought to enable a desired photonic transfer function. In such cases, many forward simulations are required along with an optimization strategy to find the optimal solution [266]. Machine learning tools greatly increase the speed of forward design, and thereby also enable rapid inverse design when coupled with techniques such as adjoint methods.

Among the most popular class of machine learning algorithms are discriminative artificial neural networks, which specify nonlinear mappings between input and output variables using matrix multiplication, neuron-based processing, and nonlinear activation functions [267]. Compared with traditional electromagnetic solvers, discriminative neural networks can evaluate forward problems orders of magnitude faster [268]. Generative neural networks using latent random variable inputs have also become popular, producing one-to-many photonic mappings that enable rapid simulation of a distribution of device layouts. In addition, several other machine learning techniques have been explored and used successfully to model photonic devices and systems [269]. An ever-increasing range of photonic devices and systems have now be successfully modelled using machine learning, ranging from integrated photonic devices [268] to ultrafast photonic systems [270] and many more.

A more recent application of machine learning is for quantum photonic systems (figure 37), where techniques are being developed to solve Schrodinger’s equation rather than Maxwell’s equations [271]. An exponential number of terms describing a quantum state can be encoded in a neural network with a polynomial number of qubits, thereby enabling efficient quantum photonic tasks such as quantum state tomography [272].

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There are several significant challenges and opportunities for machine learning in classical and quantum photonics. Among the most formidable is improved model training, which currently requires large datasets and significant up-front computational cost. While traditional direct solvers can be used to generate datasets, future efforts would be greatly benefitted by community collaboration to generate data sets and develop transfer learning techniques amenable to a wide class of photonic simulations. Community efforts to construct better benchmarking problems to assess new models is also needed.

Another related challenge is the residual uncertainty in the solutions provided by machine learning tools, and the relative difficulty of interpreting the results. Even the most carefully trained models are known to be at risk of diverging solutions within data points. Integrating the known structure of the underlying physical models (such as Schrodinger and Maxwell equations) with machine learning training algorithms, loss functions, and the resulting models may be the key to increasing the interpretability of the models, mitigating errors, and increasing training speed. Faster conventional solvers will also be helpful for model generation and verification. There continues to be rapid advances in forward solutions in the form of compact models and abstractions, many of which incorporate machine learning as subroutines [273].

Future efforts will also focus on incorporating more degrees of freedom and system complexity in machine learning models. Currently, most models include outputs such as reflection, transmission, scattering, absorption etc, but opportunities exist for incorporating additional properties to fully model the optical response, such phase, angular momentum, trajectories, nonlinearities, topology, and field distributions. Furthermore, opportunities exist of incorporating global optimizations that include elements of fabrication and experimental testing variables, and find hidden features and adaptations as the model is exposed to new data.

In the field of machine learning for quantum photonics, there is a need to improve optimization techniques and strategies. For example, only recently have viable techniques been introduced to find the quantum equivalent of the classical gradients used in most model optimizations [274], and further generalization as still sought. Another exciting research direction is the emerging ability to use machine learning models to suggest new and interesting quantum experiments [275].

Finally, enormous potential exists in developing improved photonic hardware to train and implement machine learning models. A major bottleneck using traditional hardware is the interconnect speed among neurons, which would be greatly enhanced using photonics, with a significant resulting societal impact. Quantum photonic implementations of neural networks may also greatly improve the ability to the enormous multi-dimensional datasets generated by quantum computers.

In summary, machine learning has become a vital tool for both classical and quantum photonic systems. It is anticipated that the field will continue to grow and have increasing impact.

This work is supported by the National Science Foundation under Grant No. 1941583.