Table of contents

Sources of broadband quantum correlated photons present a valuable resource for quantum metrology, sensing, and communication. Here, we report the generation of spectrally broadband correlated photons from frequency nondegenerate spontaneous parametric down-conversion in a custom-designed lithium niobate superlattice. The superlattice induces a nonlinear interference between the pump, signal and idler, resulting in an experimentally observed comb-like emission spanning 0.060 μm and 1.4 μm of spectral bandwidth at 0.647 μm and 3.0 μm wavelengths, respectively. While this broad mid-infrared bandwidth is attractive to quantum metrology and sensing due to the enablement of fast spectral multiplexing for data acquisition, the comb-like structure, achieved without an input frequency comb, offers targeted frequencies for quantum communication applications. In addition to useful technological applications, our concept offers an interesting analogy between optical diffraction in quantum and classical optics.

Modern comagnetometry is—in absolute energy units—the most sensitive experimental technique for measuring the energy splitting between quantum states, with certain implementations measuring the nuclear spin-up/spin-down splitting at the 10⁻²⁶ eV level. By measuring and subtracting the leading magnetic effects on the spins, comagnetometry can be used to study non-standard-model spin interactions. New physics scenarios that comagnetometers can probe include EDMs, violations of Lorentz invariance, Goldstone bosons from new high-energy symmetries, spin-dependent and CP-violating long-range forces, and axionic dark matter. We describe the many implementations that have been developed and optimized for these applications, and consider the prospects for improvements in the technique. Based purely on existing technology, there is room for several orders of magnitude in further improvement in statistical sensitivity. We also evaluate sources of systematic error and instability that may limit attainable improvements.

The QCD axion is a particle postulated to exist since the 1970s to explain the strong-CP problem in particle physics. It could also account for all of the observed dark matter in the Universe. The axion resonant interaction detection experiment (ARIADNE) intends to detect the QCD axion by sensing the fictitious 'magnetic field' created by its coupling to spin. Short-range axion-mediated interactions can occur between a sample of laser-polarized ³He nuclear spins and an unpolarized source-mass sprocket. The experiment must be sensitive to magnetic fields below the 10⁻¹⁹ T level to achieve its design sensitivity, necessitating tight control of the experiment's magnetic environment. We describe a method for controlling three aspects of that environment which would otherwise limit the experimental sensitivity. Firstly, a system of superconducting magnetic shielding is described to screen ordinary magnetic noise from the sample volume at the 10⁸ level, which should be sufficient to reduce the contribution of Johnson noise in the sprocket-shaped source mass, expected to be at the 10⁻¹² T$/\sqrt{\mathrm{H}\mathrm{z}}$ level, to below the threshold for signal detection. Secondly, a method for reducing magnetic field gradients within the sample up to 10² times is described, using a simple and cost-effective design geometry. Thirdly, a novel coil design is introduced which allows the generation of fields similar to those produced by Helmholtz coils in regions directly abutting superconducting boundaries. This method allows the nuclear Larmor frequency of the sample to be tuned to match the axion field modulation frequency set by the sprocket rotation. Finally, we experimentally investigate the magnetic shielding factor of sputtered thin-film superconducting niobium on quartz substrates for various geometries and film thicknesses relevant for the ARIADNE axion experiment using SQUID magnetometry. The methods may be generally useful for magnetic field control near superconducting boundaries in other experiments where similar considerations apply.

Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for quantum simulation. Hybrid classical quantum algorithms such as the variational quantum algorithms have been proposed to effectively use current term quantum devices. One promising approach to quantum simulation in the noisy intermediate-scale quantum (NISQ) era is the diagonalisation based approach, with some of the promising examples being the subspace variational quantum simulator (SVQS), variational fast forwarding (VFF), fixed-state variational fast forwarding (fs-VFF), and the variational Hamiltonian diagonalisation (VHD) algorithms. However, these algorithms require a feedback loop between the classical and quantum computers, which can be a crucial bottleneck in practical application. Here, we present the classical quantum fast forwarding (CQFF) as an alternative diagonalisation based algorithm for quantum simulation. CQFF shares some similarities with SVQS, VFF, fs-VFF and VHD but removes the need for a classical-quantum feedback loop and controlled multi-qubit unitaries. The CQFF algorithm does not suffer from the barren plateau problem and the accuracy can be systematically increased. Furthermore, if the Hamiltonian to be simulated is expressed as a linear combination of tensored-Pauli matrices, the CQFF algorithm reduces to the task of sampling some many-body quantum state in a set of Pauli-rotated bases, which is easy to do in the NISQ era. We run the CQFF algorithm on existing quantum processors and demonstrate the promise of the CQFF algorithm for current-term quantum hardware. We compare CQFF with Trotterization for a XY spin chain model Hamiltonian and find that the CQFF algorithm can simulate the dynamics more than 10⁵ times longer than Trotterization on current-term quantum hardware. This provides a 10⁴ times improvement over the previous record.

We propose an electromechanical scheme where the electronic degrees of freedom of boron vacancy color centers hosted by a hexagonal boron nitride (hBN) nanoribbon are coupled for quantum information processing. The mutual coupling of color centers is provided via their coupling to the mechanical motion of the ribbon, which in turn stems from the local strain. The coupling strengths are computed by performing ab initio calculations. The density functional theory results for boron vacancy centers on boron nitride monolayers reveal a huge strain susceptibility. In our analysis, we take into account the effect of all flexural modes and show that despite the thermal noise introduced through the vibrations one can achieve steady-state entanglement between two and more number of qubits that survives even at room temperature. Moreover, the entanglement is robust against mis-positioning of the color centers. The effective coupling of color centers is engineered by positioning them in the proper positions. Hence, one is able to tailor stationary graph states. Furthermore, we study the quantum simulation of the Dicke–Ising model and show that the phonon non-equilibrium phase transition occurs even for a finite number of color centers. Given the steady-state nature of the proposed scheme and accessibility of the electronic states through optical fields, our work paves the way for the realization of steady-state quantum information processing with color centers in hBN membranes.

An important part of reaping computational advantage from a quantum computer is to reduce the quantum resources needed to implement a desired quantum algorithm. Quantum algorithms that are too large to be practical on noisy intermediate scale quantum devices will require fault-tolerant error correction. This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more resources than the other gates in the gate set. More specifically, in this paper we consider the group of unitaries that can be exactly implemented by a quantum circuit consisting of the Clifford + T gate set. The Clifford + T gate set is a universal gate set and in this group, using state-of-the-art surface codes, the T gate is by far the most expensive component to implement fault-tolerantly. So it is important to minimize the number of T gates necessary for a fault-tolerant implementation. Our primary interest is to compute a circuit for a given n-qubit unitary U, using the minimum possible number of T gates (called the T-count of unitary U). We consider the problem COUNT-T, the optimization version of which aims to find the T-count of U. In its decision version the goal is to decide if the T-count is at most some positive integer m. Given an oracle for COUNT-T, we can compute a T-count-optimal circuit in time polynomial in the T-count and dimension of U. We give a provable classical algorithm that solves COUNT-T (decision) in time $O\left({N}^{2(c-1)\lceil \frac{m}{c}\rceil }\enspace \mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}(m,N)\right)$ and space $O\left({N}^{2\lceil \frac{m}{c}\rceil }\enspace \mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}(m,N)\right)$, where N = 2ⁿ and c ⩾ 2. This gives a space-time trade-off for solving this problem with variants of meet-in-the-middle techniques. We also introduce an asymptotically faster multiplication method that shaves a factor of N^0.7457 off of the overall complexity. Lastly, beyond our improvements to the rigorous algorithm, we give a heuristic algorithm that outputs a T-count-optimal circuit and has space and time complexity poly(m, N), under some assumptions. In our heuristic algorithm we developed a novel way of pruning the search space. While our heuristic method still scales exponentially with the number of qubits (though with a lower exponent), there is a large improvement by going from exponential to polynomial scaling with m. We implemented our heuristic algorithm with up to 4 qubit unitaries and obtained a significant improvement in time. For all benchmark and random unitaries we studied, the T-count returned by our algorithm is at most the T-count of their circuits shown in previous papers.

Quantum computers based on solid state qubits have been a subject of rapid development in recent years. In current noisy intermediate-scale quantum technology, each quantum device is controlled and characterised through a dedicated signal line between room temperature and base temperature of a dilution refrigerator. This approach is not scalable and is currently limiting the development of large-scale quantum system integration and quantum device characterisation. Here we demonstrate a custom designed cryo-CMOS multiplexer operating at 32 mK. The multiplexer exhibits excellent microwave properties up to 10 GHz at room and millikelvin temperatures. We have increased the characterisation throughput with the multiplexer by measuring four high-quality factor superconducting resonators using a single input and output line in a dilution refrigerator. Our work lays the foundation for large-scale microwave quantum device characterisation and has the perspective to address the wiring problem of future large-scale quantum computers.

Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features especially for high-dimensional and multipartite quantum systems. In this work, we exploit the convexity of samples without the desired quantum features and design an unsupervised machine learning method to detect the presence of such features as anomalies. Particularly, in the context of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from two-qubit to ten-qubit systems, that our network is able to achieve high detection accuracy which is above 97.5% on average. Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, and thus our work could provide a powerful tool to extract quantum features hidden in multipartite quantum data.

The high-dimensional quantum system greatly improve the quantum channel capacity and information storage space, and achieve high-dimensional quantum information transmission, which enhance the speed of quantum computing and quantum information processing. In this paper, a high-dimensional quantum teleportation protocol without information loss is proposed. We consider pre-sharing a high-dimensional non-maximum entangled state as a quantum channel between sender and receiver. By adding auxiliary particle and performing high-dimensional local operations, it is possible to achieve high-dimensional quantum teleportation without information loss. Simultaneously, we apply the protocol to butterfly network, and propose a novel high-dimensional quantum network coding based on prediction mechanism. In our scheme, we use Z-{|0⟩, |1⟩} basis to predict the transmission of high dimensional states over the butterfly network. When the prediction is successful, the deterministic transmission of high-dimensional quantum states can be realized over the butterfly network. Our scheme greatly saves the usage of quantum and classical channels, which improves the utilization efficiency of both channels.

Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan et al 2019 Quantum 4 296] found that the lowest resource costs were achieved by split-operator Trotterization combined with the fast-fermionic Fourier transform (FFFT) on an L × L lattice with length L = 2^k. On lattices with length L ≠ 2^k, Givens rotations can be used instead of the FFFT but lead to considerably higher resource costs. We present a new analytic approach to bounding the simulation error due to Trotterization that provides much tighter bounds for the split-operator FFFT method, leading to 16× improvement in error bounds. Furthermore, we introduce plaquette Trotterization that works on any size lattice and apply our improved error bound analysis to show competitive resource costs. We consider a phase estimation task and show plaquette Trotterization reduces the number of non-Clifford gates by a factor 5.5× to 9× (depending on the parameter regime) over the best previous estimates for 8 × 8 and 16 × 16 lattices and a much larger factor for other lattice sizes not of the form L = 2^k. In conclusion, we find there is a potentially useful application for fault-tolerant quantum computers using around one million Toffoli gates.

Quantum information platforms made great progress in the control of many-body entanglement and the implementation of quantum error correction, but it remains a challenge to realize both in the same setup. Here, we propose a mixture of two ultracold atomic species as a platform for universal quantum computation with long-range entangling gates, while providing a natural candidate for quantum error-correction. In this proposed setup, one atomic species realizes localized collective spins of tunable length, which form the fundamental unit of information. The second atomic species yields phononic excitations, which are used to entangle collective spins. Finally, we discuss a finite-dimensional version of the Gottesman–Kitaev–Preskill code to protect quantum information encoded in the collective spins, opening up the possibility to universal fault-tolerant quantum computation in ultracold atom systems.

Near term quantum computers suffer from the presence of different noise sources. In order to mitigate for this effect and acquire results with significantly better accuracy, there is the urge of designing efficient error correction or error mitigation schemes. The cost of such techniques is usually high in terms of resource requirements, either in hardware or at the algorithmic level. In this work, we follow a pragmatic approach and we use repetition codes as scalable schemes with the potential to provide more accurate solutions to problems of interest in quantum chemistry and physics. We investigate different repetition code layouts and we propose a circular repetition scheme with connectivity requirements that are native on IBM Quantum hardware. We showcase our approach in multiple IBM Quantum devices and validate our results using a simplified theoretical noise model. We highlight the effect of using the proposed scheme in an electronic structure variational quantum eigensolver calculation and in the simulation of time evolution for a quantum Ising model.

This paper proposes a machine learning method to characterize photonic states via a simple optical circuit and data processing of photon number distributions, such as photonic patterns. The input states consist of two coherent states used as references and a two-mode unknown state to be studied. We successfully trained supervised learning algorithms that can predict the degree of entanglement in the two-mode state as well as perform the full tomography of one photonic mode, obtaining satisfactory values in the considered regression metrics.

Quantum states of light can enable sensing configurations with sensitivities beyond the shot-noise limit. In order to better take advantage of available quantum resources and obtain the maximum possible sensitivity, it is necessary to determine fundamental sensitivity limits for different possible configurations for a given sensing system. Here, due to their wide applicability, we focus on optical resonance sensors, which detect a change in a parameter of interest through a resonance shift. We compare their fundamental sensitivity limits set by the quantum Cramér–Rao bound (QCRB) based on the estimation of changes in transmission or phase of a probing bright two-mode squeezed state (bTMSS) of light. We show that the fundamental sensitivity results from an interplay between the QCRB and the transfer function of the system. As a result, for a resonance sensor with a Lorentzian lineshape a phase-based scheme outperforms a transmission-based one for most of the parameter space; however, this is not the case for lineshapes with steeper slopes, such as higher order Butterworth lineshapes. Furthermore, such an interplay results in conditions under which the phase-based scheme provides a higher sensitivity but a smaller degree of quantum enhancement than the transmission-based scheme. We also study the effect of losses external to the sensor on the degree of quantum enhancement and show that for certain conditions, probing with a classical state can provide a higher sensitivity than probing with a bTMSS. Finally, we discuss detection schemes, namely optimized intensity-difference and optimized homodyne detection, that can achieve the fundamental sensitivity limits even in the presence of external losses.

Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation (GQC) on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric phase, π/8 and Hadamard gates can be obtained as 99.93%, 99.95% and 99.95%, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as 99.87%. Therefore, our scheme provides a new perspective for GQC, making it more promising in the application of large-scale fault-tolerant quantum computation.

Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealing have centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these advances has centered around the development of driver Hamiltonians that commute with the constraints of an optimization problem—allowing for another avenue to satisfying those constraints instead of imposing penalty terms for each of them. In particular, the approach is able to use sparser connectivity to embed several practical problems on quantum devices in comparison to the standard approach of using penalty terms. However, designing the driver Hamiltonians that successfully commute with several constraints has largely been based on strong intuition for specific problems and with no simple general algorithm for generating them for arbitrary constraints. In this work, we develop a simple and intuitive algebraic framework for reasoning about the commutation of Hamiltonians with linear constraints—one that allows us to classify the complexity of finding a driver Hamiltonian for an arbitrary set of linear constraints as NP-complete. Because unitary operators are exponentials of Hermitian operators, these results can also be applied to the construction of mixers in the quantum alternating operator ansatz framework.

The satellite-based measurement-device-independent quantum key distribution can promote the realization of quantum communication networks. Under the condition of the limited data set, it is necessary to optimize all parameters. For communication networks, real-time prediction and optimization are also indispensable. With the development of machine learning, cross-combination with machine learning has also become the mainstream of parameter optimization in various disciplines. This paper discusses the asymmetric MDI-QKD based on the satellite in the case of statistical fluctuations, and uses the local search algorithm to achieve full parameter optimization under the condition of considering the probability of sending the signal. Compared with fixed related parameters, the key rate is increased by an order of magnitude. On this basis, random forest is used to predict the high-precision optimal parameters, thereby eliminating the simulation and iteration required by the search method to meet the real-time optimization of the future QKD network.

We study a quantum many-body system of attracting bosons confined in a ring-shaped potential and interrupted by a weak link. With such architecture, the system defines atomtronic quantum interference devices harnessing quantum solitonic currents. We demonstrate that the system is characterized by the specific interplay between the interaction and the strength of the weak link. In particular, we find that, depending on the operating conditions, the current can be a universal function of the relative size between the strength of the impurity and interaction. The low lying many-body states are studied through a quench dynamical protocol that is the atomtronic counterpart of Rabi interferometry. With this approach, we demonstrate how our system defines a two level system of coupled solitonic currents. The current states are addressed through the analysis of the momentum distribution.

Quantum gates are essential for the realization of quantum computer and have been implemented in various types of two-level systems. However, high-dimensional quantum gates are rarely investigated both theoretically and experimentally even that high-dimensional quantum systems exhibit remarkable advantages over two-level systems for some quantum information and quantum computing tasks. Here we experimentally demonstrate the four-dimensional X gate and its unique higher orders with the average conversion efficiency 93%. All these gates are based on orbital-angular-momentum degree of freedom (DoF) of single photons. Besides, a set of controlled quantum gates is implemented by use of polarization DoF. Our work is an important step toward the goal of achieving arbitrary high-dimensional quantum circuit and paves a way for the implementation of high-dimensional quantum communication and computation.

The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors, while demanding certainty leads to some inconclusiveness. One of the most fundamental strategies developed for this task is the optimal unambiguous measurement. It encompasses conclusive results, which allow for error-free state retrodictions with the maximum success probability, and inconclusive results, which are discarded for not allowing perfect identifications. Interestingly, in high-dimensional Hilbert spaces the inconclusive results may contain valuable information about the input states. Here, we theoretically describe and experimentally demonstrate the discrimination of nonorthogonal states from both conclusive and inconclusive results in the optimal unambiguous strategy, by concatenating a minimum-error measurement at its inconclusive space. Our implementation comprises four- and nine-dimensional spatially encoded photonic states. By accessing the inconclusive space to retrieve the information that is wasted in the conventional protocol, we achieve significant increases of up to a factor of 2.07 and 3.73, respectively, in the overall probabilities of correct retrodictions. The concept of concatenated optimal measurements demonstrated here can be extended to other strategies and will enable one to explore the full potential of high-dimensional nonorthogonal states for quantum communication with larger alphabets.

We present Qibo, a new open-source software for fast evaluation of quantum circuits and adiabatic evolution which takes full advantage of hardware accelerators. The growing interest in quantum computing and the recent developments of quantum hardware devices motivates the development of new advanced computational tools focused on performance and usage simplicity. In this work we introduce a new quantum simulation framework that enables developers to delegate all complicated aspects of hardware or platform implementation to the library so they can focus on the problem and quantum algorithms at hand. This software is designed from scratch with simulation performance, code simplicity and user friendly interface as target goals. It takes advantage of hardware acceleration such as multi-threading Central Processing Unit (CPU), single Graphics Processing Unit (GPU) and multi-GPU devices.

Estimating the difference between quantum data is crucial in quantum computing. However, as typical characterizations of quantum data similarity, the trace distance and quantum fidelity are believed to be exponentially-hard to evaluate in general. In this work, we introduce hybrid quantum–classical algorithms for these two distance measures on near-term quantum devices where no assumption of input state is required. First, we introduce the variational trace distance estimation (VTDE) algorithm. We in particular provide the technique to extract the desired spectrum information of any Hermitian matrix by local measurement. A novel variational algorithm for trace distance estimation is then derived from this technique, with the assistance of a single ancillary qubit. Notably, VTDE could avoid the barren plateau issue with logarithmic depth circuits due to a local cost function. Second, we introduce the variational fidelity estimation algorithm. We combine Uhlmann's theorem and the freedom in purification to translate the estimation task into an optimization problem over a unitary on an ancillary system with fixed purified inputs. We then provide a purification subroutine to complete the translation. Both algorithms are verified by numerical simulations and experimental implementations, exhibiting high accuracy for randomly generated mixed states.

Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify—and classically represent—their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states—which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.

Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the filtering variational quantum eigensolver which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution. Additionally we explore the use of causal cones to reduce the number of qubits required on a quantum computer. Using random weighted MaxCut problems, we numerically analyze our methods and show that they perform better than the original VQE algorithm and the quantum approximate optimization algorithm. We also demonstrate the experimental feasibility of our algorithms on a Quantinuum trapped-ion quantum processor powered by Honeywell.

Understanding the emergence of objectivity from the quantum realm has been a long standing issue strongly related to the quantum to classical crossover. Quantum Darwinism (QD) provides an answer, interpreting objectivity as consensus between independent observers. Quantum computers provide an interesting platform for such experimental investigation of QD, fulfiling their initial intended purpose as quantum simulators. Here we assess to what degree current Noisy intermediate-scale quantum devices can be used as experimental platforms in the field of QD. We do this by simulating an exactly solvable stochastic collision model, taking advantage of the analytical solution to benchmark the experimental results.

The motion of trapped atoms plays an essential role in quantum mechanical sensing, simulations and computing. Small disturbances of atomic vibrations are still challenging to be sensitively detected. It requires a reliable coupling between individual phonons and internal electronic levels that light can readout. As available information in a few electronic levels about the phonons is limited, the coupling needs to be sequentially repeated to further harvest the remaining information. We analyze such phonon measurements on the simplest example of the force and heating sensing using motional Fock states. We prove that two sequential measurements are sufficient to reach sensitivity to force and heating for realistic Fock states and saturate the quantum Fisher information for a small amount of force or heating. It is achieved by the conventionally available Jaynes–Cummings coupling. The achieved sensitivities are found to be better than those obtained from classical states. Further enhancements are expectable when the higher Fock state generation is improved. The result opens additional applications of sequential phonon measurements of atomic motion. This measurement scheme can also be directly applied to other bosonic systems including cavity QED and circuit QED.

Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. We compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM's quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y-rotations on all qubits.

We propose a potentially practical scheme for the controllable single-photon transport via waveguides which are coupled to a microcavity–emitter system. The microcavity–emitter system consists of a V-type three-level emitter and two or one single-mode microcavity. A driving field is used to drive a hyperfine transition between two upper excited states of the V-type three-level emitter. Beyond chiral coupling between waveguides and microcavity–emitter system, we show that the perfectly nonreciprocal single-photon transport in a single waveguide and the single-photon router with 100% routing probability in two waveguides can be achieved. Interesting enough, whether the nonreciprocal single-photon transport or the single-photon router can be switched periodically by adjusting the phase associated with microcavity–emitter coupling strength and the driving field. The complete physical explanation of the underlying mechanism is presented.