A 12-mode Universal Photonic Processor for Quantum Information Processing

Photonic processors are pivotal for both quantum and classical information processing tasks using light. In particular, linear optical quantum information processing requires both largescale and low-loss programmable photonic processors. In this paper, we report the demonstration of the largest universal quantum photonic processor to date: a low-loss, 12-mode fully tunable linear interferometer with all-to-all coupling based on stoichiometric silicon nitride waveguides.

Linear optics quantum information processing holds great promise for solving particular problems with exponentially greater computational power than classical computers. A large collection of proposed applications can be found in the literature [25][26][27]. The recent a demonstration of a quantum advantage in a static optical system [28] shows the urgent need for programmable photonic processors.
The fundamental process of linear optics quantum information processing is quantum interference. To exploit it, a setup is needed consisting of photon sources, a photonic processor and single-photon detectors. The photons are used as information carriers and the photonic processor, formed by linear optical elements, will process quantum information by letting the photons interfere in a controlled manner. By looking at the configurations of the output samples of the photons at the detectors, the result of the photonic computation can be read out.
For photonic quantum information processing, the requirements on a photonic processor are fourfold. First, it must be largescale as this increases the complexity of the problems that can be solved. Second, it must be universal (i.e., fully-reconfigurable and with all-to-all connectivity) since this enables the implementation of arbitrary transformations mapping onto various problems. Third, it must be low-loss as otherwise the information carried by single photons is lost. Finally, as stated above, a photonic processor needs to preserve quantum interference.
In this paper, we describe a 12-mode i low-loss (end-to-end 5 dB) reconfigurable photonic processor based on stoichiometric silicon nitride waveguides, which is the largest universal photonic processor to date. We report the results of the classical and quantum characterization showing that full reconfigurability, low loss, and high-fidelity operations are achieved.
The paper is structured as follows: in section 2 the components of the 12-mode photonic processor are described; in section 3 we report the experimental results of the classical and quantum characterization of the processor; in section 4 prospects for the technology are discussed; in section 5 we derive the conclusions.

Photonic processor
In this section, we describe the main components of our 12-mode photonic processor ( Fig. 1). It consists of three parts: an integrated silicon nitride photonic chip, peripheral equipment, and the software to control its functionality.

Photonic chip
The heart of our photonic processor is a reconfigurable photonic integrated circuit based on stoichiometric silicon nitride (Si3N4) waveguides with the TripleX technology. Thanks to the chosen material platform, we achieve propagation losses as low as 0.1 dB/cm with a minimum bending radius of 100 µm. The waveguide cross-section used in the photonic processor is an asymmetric doublestripe (ADS) [29] as shown in Fig. 1a. The waveguides are designed for single-mode operation at a wavelength of 1550 nm. ADS waveguides enable low-loss coupling to standard telecom fibers using spot-size converters, where the upper silicon nitride stripe is removed by adiabatic tapering [29].
The reconfigurability of the photonic processor is achieved by exploiting the thermo-optic via resistive heating of 1 mmlong platinum phase shifters. Using these thermo-optic phase shifters, a phase shift is achieved at # ≅ 10 V, corresponding to an electrical power of ~385 mW per element.
The functional design of our processor is presented in Fig. 1b. An optical unit cell, composed of a tunable beam splitter (blue line) and a phase shifter (red line) on the bottom output mode, is repeated 66 times over a square topology of 12 input/output modes and circuit depth of 12. Twenty-four additional phase shifters are distributed across the inputs and outputs for sub-wavelength delay compensation and external phase tuning. In total, the processor contains 156 phase shifters (of which 24 are redundant and not connected). The tunable beam splitters are implemented by Mach-Zehnder interferometers (MZI) consisting of two 50:50 directional couplers (black lines in Fig. 1b) and an internal phase shifter, q, followed by an external phase shifter, f, at the bottom output mode. Each unit cell represents a node of the large-scale interferometer where light can interfere.

Peripherals
The photonic processor presented above is embedded in a control box that includes electronic and temperature control modules ( Fig. 1c and 1d). The reconfigurable photonic integrated circuit is optically packaged with polarization-maintaining (PM) fiber arrays for the in-and out-coupling of light. For ease of access the input and output fibers are fixed to the front panel of the control box via PM mating sleeves. We measure an average loss for the 24 PM mating sleeves of about 0.18 dB/connector.
A printed circuit board (PCB) was fabricated and wire-bonded to the photonic processor. A total of 132 voltage drivers are connected to the PCB enabling the independent tuning of each thermo-optic phase shifter, achieved via serial communication with a standard pc.
Temperature control and stability of the processor is achieved by active cooling. A thermo-electric Peltier element is placed beneath the sub-mount of the packaged processor, i.e., a metallic mount holding the processor, the fiber arrays and the PCB. The Peltier element favors the heat transfer in the vertical direction, from the on-chip phase shifters to the heat-sink. To further increase the heat capacity of the system, water cooling can also be installed.

Software -Control system
The optical transmission through our photonic processor is described by a matrix, S, relating the output electric fields to the input ones &'( = +, . The matrix S is given by the product of two-mode matrices Sm,n of each unit cell between mode m and n. Considering a unit cell as in Fig. 1b with pairs of ideal and symmetric 50:50 directional couplers (k = 0.5), we find that ',+(_./00 ( , ) = 6 7 8 where q is the internal phase of the MZI and f is the external phase. By varying q and f over 2p it is possible to perform any transformation in the special unitary group, SU (2). It is important to note that the action of the processor is always described by the same classical scattering matrix S independently of the nature of the input state, i.e., either classical electric field amplitudes or photonnumber states. Therefore, to know the transmission matrix, it is sufficient to characterize the processor classically. In the case of quantum input light, the formalism becomes W &'( = W +, where now the scattering matrix relates the ladder operators instead of classical electric field amplitudes [30]. The combination of quadratically many Sm,n allows the implementation of any complexvalued unitary transformations U. We can decompose any arbitrary unitary transformation U into sets of (q, f)m,n belonging to specific unit cells between mode m and n of our processor [23,24]. Assigning these (q, f)m,n to the corresponding scattering matrix Sm,n and multiplying them in the order of light propagation through the processor, the exact optical response corresponding to U will be reproduced.

System performance
In this section, we report the classical and quantum characterization of the 12-mode photonic processor. The experimental setup is depicted in Fig. 2.
For classical characterization of the processor we use a CW diode laser at 1550 nm (2 mW output power-LP1550 PAD). A PM fiber switch can be used to facilitate the procedure of characterization switching the input light across all the 12 inputs. For intensity measurements we use a set of InGaAs photodiodes each mounted on a FC/PC bulkhead (Thorlabs FGA01FC) (Fig. 2a). The output signal of the QuiX hardware, impinging on the PD array, is acquired and read out via an NI BNC-2090A and USB-6211 card.
For quantum characterization a 2 mm ppKTP crystal emitting collinear frequency- degenerate cross-polarized single-photon pairs is pumped with a Ti:Sapphire (Tsunami, Spectra Physics) mode-locked laser with a center wavelength of 775 nm. The photons are measured on superconducting nanowire single-photon detectors (Photon Spot) (Fig.  2b). Coupling between the light source and the QuiX hardware is done via polarization maintaining fibers.

Classical response
First, we report the classical characterization of the processor. This comprises the calibration of all the tunable elements and the total transmission of the processor, as shown in Fig. 3(a, b, c). Specific measurement protocols are used to characterize the tunable beam splitters (TBS) and phase shifters (PS).
In Fig. 3a we show the calibration of one of the on-chip heaters as, for example, the one belonging to a TBS. Both outputs of the TBS are monitored while only the internal phase is varied (inset Fig.1b). This is done by applying a varying voltage, V, to the thermooptic phase shifter. The same procedure is adopted for characterizing the PSs. By following a specific order, we characterize the entire processor and find that all the 132 thermo-optic phase shifters are tunable over more than 2p phase range with high extinction ratio. In this way, we achieve full control over the processor.
In Fig. 3b, we report the insertion loss matrix of the processor. The insertion loss matrix includes both the fiber-to-chip-to-fiber coupling losses and the on-chip propagation loss. It excludes thus the aforementioned connector loss of 0.18 dB/connector. The reader can clearly see that there is one input channel that shows higher losses than the others. This is confirmed by inspection of one of the fibers, which turned out to be damaged. The optimal transmission for this input channel can be easily retrieved by exchanging the damaged fiber. On average, the processor shows an insertion loss of ~5 dB where ~0.8 dB comes from propagation loss and the remaining ~4.2 dB are coupling losses.
Finally, to confirm the universality and control of the processor, we perform a large variety of 12-dimensional unitary transformations as summarized in Fig. 3(c, d,  e). For each target transformation + , we measure the corresponding experimental output intensity distribution | /_`| 7 . We We perform unitary transformations spanning various applications such as permutation (P) and Haar-random matrices, high-dimensional Pauli-X gates (X) and optical switching matrices (S). Furthermore, to ultimately illustrate our full control over our processor we implement the letters Q and X of our company name QuiX.
In Fig. 3c, we report, as an example, the target (theory) (g , (g and (g matrix (top rowfrom left to right) and their corresponding experimental implementations (bottom row). Fig. 3d shows the distribution of fidelities for 1000 Haar random unitaries. We note that an increase in the complexity of the optical transformation is associated with a decrease in fidelity, as it is natural to expect. Since by definition Haar matrices cover the space of unitary transformations in a uniform way, we expect the fidelity for this set to be representative for an arbitrary transformation. Finally, Fig. 3e reports the measurements of the first and last letter of the company name QuiX. The results are summarized in Table 1.

Quantum response
After having demonstrated full control of the processor via the classical response characterization, we attach the QuiX hardware to the quantum light source as shown in Fig.  2b. Quantum interference experiments were performed across the whole photonic processor evaluating to what extent the processor is able to preserve the indistinguishability of the input single photons. This measurement tests all sources of which-way information, such as pathdependent dispersion.
The single-photon source is characterized separately by running a Hong-Ou-Mandel (HOM) [31] interference experiment over a tunable fiber-splitter that gives a visibility of 0.94.
By choosing inputs pairwise, we run Hong-Ou-Mandel (HOM) interference experiments on every single TBS on the processor (Fig. 4) Fig. 4). We obtain an average visibility of jk/ = 0.923. We observe from Fig. 4c that the distribution of the HOM visibility is rather random across the UMI confirming the absence of any systematic error in the processor. Some TBSs, e.g. # 136, 140 and 145, present a low visibility of the quantum interfere: this is due to an imperfectly optimized 50:50 splitting ratio setting of these TBSs, which reduces the HOM visibility.
Comparing the reference and the measured average on-chip visibility we can conclude that the processor does not affect the spectraltemporal indistinguishability of the signal and idler photons of the photon pair as coming out from the source. The on-chip visibility is ultimately limited by the source itself.

Discussion
Finally, we discuss the future prospects of our technology. With this 12 x 12 processor, we have not exhausted the capabilities of the SiN platform; we anticipate producing larger processors with higher fidelity and lower optical loss in the future. We discuss these issues in turn.
The fidelity of the unitary transformations can be improved by correcting and compensating for crosstalk, upgrading both the hardware and the software. Examples can be found in the literature [32][33][34]. Furthermore, the compensation of non-ideal extinction ratio of the TBS will also improve the fidelity. This can be obtained by redundancy [35,36].
The insertion loss of the system can be further reduced by optimal waveguide engineering, to enable even a greater scalability of our technology. By optimal waveguide tapering the coupling losses can be reduced down to ~1 dB [29]. With these modifications, the system will become practical as a photonic processor for quantum interference experiments in the regime where a quantum advantage exists [28]. The integration of single-photon sources, by exploiting the thirdorder nonlinearity of silicon nitride, and detectors will help further in reducing the coupling losses [37][38][39].
Valid alternatives to thermo-optic tuning are available such as the implementation of liquid crystals [40,41], phase-changing materials [42] and stress-optic tuning [43,44] in order to reduce the power consumption. The latter additionally has the advantage to operate at cryogenic temperatures [45]. Operating the chip at cryogenic temperatures would permit direct integration with both solid-state singlephoton sources [46] and superconducting single-photon detectors [38,39].

Conclusions
In this paper we have reported a 12-mode fully reconfigurable universal photonic processor based on silicon nitride waveguides. The processor is embedded into a control system that enables remote access to its optical functionality and reconfigurability. The system operates at 1550 nm with insertion loss of ~5 dB (averaged over all the optical paths). All the 132 tunable elements of the processor provide more than 2 phase shift with high extinction ratio. High fidelities are measured over a set of 1036 unitary transformations. Quantum interference of high visibility is replicable across the entire processor, i.e., the indistinguishability of photons is preserved.
The photonic processor presented here is the largest low-loss plug-and-play universal square photonic processor to date, enabling fully-reconfigurable unitary transformations across 12 inputs and through 12 layers of depth.