Experimental realization of any discrete unitary operator

Phase-shift determination for a 4 × 4 intelligent photonic neural network with compatible learning

Intelligent photonic circuits (IPCs) tuned with an appropriate phase-shift vector could enable a photonic intelligent matrix possibly implemented in multiple neural layers for a task-oriented topologies. A photonic Mach-Zehnder Interferometer (MZI) is a fundamental photonic component in IPCs, whose matrix representation could be broadcasted into an arbitrary matrix that is equipped with an optimized phase-shift vector. The initialized MZIs' phases are tentatively probed between analytical elements and a digital weight matrix that is learned from samples with efficient compatible learning for complex-valued neural networks. Nonlinear least squares is utilized to formulate a phase determination system to refine the optimal phase-shift solutions. The robustness of phase determination system for photonic neural networks is discussed in detail. For a preliminary implementation, a basic 4×4 intelligent photonic neural network is utilized to verify the proof of concept on phase-shift determination in IPC through numerical experiments.

Tailor-made unitary operations using dielectric metasurfaces

Qubit operation belonging to unitary transformation is the fundamental operation to realize quantum computing and information processing. Here, we show that the complex and flexible light-matter interaction between dielectric metasurfaces and incident light can be used to perform arbitrary U(2) operations. By incorporating both coherent spatial-mode operation together with two polarizations on a single metasurface, we further extend the discussion to single-photon two-qubit U(4) operations. We believe the efficient usage of metasurfaces as a potential compact platform can simplify optical qubit operation from bulky systems into conceptually subwavelength elements.

Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor

Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.

Cascaded optical resonator-based programmable photonic integrated circuits

Programmable photonic integrated circuits have mainly been developed based on the single wavelength channel operation of fundamental building blocks consisting of Mach-Zehnder interferometers (MZIs) with tunable phase shifters. We propose and study optical circuit models consisting of cascaded optical resonators that enable the independent operation of multiple wavelength channels in a more compact footprint than the conventional MZIs. By adopting experimental values reported for silicon micro-ring resonators, the fidelities of different types of 2×2 unitary transformations and higher-dimensional unitary transformations are examined by employing the Reck algorithm and the Clements algorithm.

Creating and concentrating quantum resource states in noisy environments using a quantum neural network

Quantum information processing tasks require exotic quantum states as a prerequisite. They are usually prepared with many different methods tailored to the specific resource state. Here we provide a versatile unified state preparation scheme based on a driven quantum network composed of randomly-coupled fermionic nodes. The output of such a system is then superposed with the help of linear mixing where weights and phases are trained in order to obtain desired output quantum states. We explicitly show that our method is robust and can be utilized to create almost perfect maximally entangled, NOON, W, cluster, and discorded states. Furthermore, the treatment includes energy decay in the system as well as dephasing and depolarization. Under these noisy conditions we show that the target states are achieved with high fidelity by tuning controllable parameters and providing sufficient strength to the driving of the quantum network. Finally, in very noisy systems, where noise is comparable to the driving strength, we show how to concentrate entanglement by mixing more states in a larger network.

An optical neural chip for implementing complex-valued neural network

Complex-valued neural networks have many advantages over their real-valued counterparts. Conventional digital electronic computing platforms are incapable of executing truly complex-valued representations and operations. In contrast, optical computing platforms that encode information in both phase and magnitude can execute complex arithmetic by optical interference, offering significantly enhanced computational speed and energy efficiency. However, to date, most demonstrations of optical neural networks still only utilize conventional real-valued frameworks that are designed for digital computers, forfeiting many of the advantages of optical computing such as efficient complex-valued operations. In this article, we highlight an optical neural chip (ONC) that implements truly complex-valued neural networks. We benchmark the performance of our complex-valued ONC in four settings: simple Boolean tasks, species classification of an Iris dataset, classifying nonlinear datasets (Circle and Spiral), and handwriting recognition. Strong learning capabilities (i.e., high accuracy, fast convergence and the capability to construct nonlinear decision boundaries) are achieved by our complex-valued ONC compared to its real-valued counterpart.

Efficient Simulation of Loop Quantum Gravity: A Scalable Linear-Optical Approach

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is loop quantum gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spin-foam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the bounded-error quantum polynomial time class, which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers, which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer that can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.

Two-photon interference: the Hong-Ou-Mandel effect

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

Experimental Parity-Time Symmetric Quantum Walks for Centrality Ranking on Directed Graphs

Using quantum walks (QWs) to rank the centrality of nodes in networks, represented by graphs, is advantageous compared to certain widely used classical algorithms. However, it is challenging to implement a directed graph via QW, since it corresponds to a non-Hermitian Hamiltonian and thus cannot be accomplished by conventional QW. Here we report the realizations of centrality rankings of a three-, a four-, and a nine-vertex directed graph with parity-time (PT) symmetric quantum walks by using high-dimensional photonic quantum states, multiple concatenated interferometers, and dimension dependent loss to achieve these. We demonstrate the advantage of the QW approach experimentally by breaking the vertex rank degeneracy in a four-vertex graph. Furthermore, we extend our experiment from single-photon to two-photon Fock states as inputs and realize the centrality ranking of a nine-vertex graph. Our work shows that a PT symmetric multiphoton quantum walk paves the way for realizing advanced algorithms.

Physics successfully implements Lagrange multiplier optimization

Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the Principle of Least Action; the Principle of Minimum Power Dissipation, also called Minimum Entropy Generation; and the Variational Principle. Physics also has Physical Annealing, which, of course, preceded computational Simulated Annealing. Physics has the Adiabatic Principle, which, in its quantum form, is called Quantum Annealing. Thus, physical machines can solve the mathematical problem of optimization, including constraints. Binary constraints can be built into the physical optimization. In that case, the machines are digital in the same sense that a flip-flop is digital. A wide variety of machines have had recent success at optimizing the Ising magnetic energy. We demonstrate in this paper that almost all those machines perform optimization according to the Principle of Minimum Power Dissipation as put forth by Onsager. Further, we show that this optimization is in fact equivalent to Lagrange multiplier optimization for constrained problems. We find that the physical gain coefficients that drive those systems actually play the role of the corresponding Lagrange multipliers.

Setting Up Experimental Bell Tests with Reinforcement Learning

Finding optical setups producing measurement results with a targeted probability distribution is hard, as a priori the number of possible experimental implementations grows exponentially with the number of modes and the number of devices. To tackle this complexity, we introduce a method combining reinforcement learning and simulated annealing enabling the automated design of optical experiments producing results with the desired probability distributions. We illustrate the relevance of our method by applying it to a probability distribution favouring high violations of the Bell-Clauser-Horne-Shimony-Holt (CHSH) inequality. As a result, we propose new unintuitive experiments leading to higher Bell-CHSH inequality violations than the best currently known setups. Our method might positively impact the usefulness of photonic experiments for device-independent quantum information processing.

Observing Geometry of Quantum States in a Three-Level System

In quantum mechanics, geometry has been demonstrated as a useful tool for inferring nonclassical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the quantum state space onto the Euclidean space via measurements of observables on the system. Despite the great success of this method in studying two-level quantum systems (qubits) with the celebrated Bloch sphere representation, it is still difficult to reveal the geometry of multidimensional quantum systems. Here we report the first experiment measuring the geometry of such projections beyond the qubit. Specifically, we observe the joint numerical ranges of a triple of observables in a three-level photonic system, providing a complete classification of these ranges. We further show that the geometry of different classes reveals ground-state degeneracies of a Hamiltonian as a linear combination of the observables, which is related to quantum phases in the thermodynamic limit. Our results offer a versatile geometric approach for exploring the properties of higher-dimensional quantum systems.

Programmable photonic circuits

The growing maturity of integrated photonic technology makes it possible to build increasingly large and complex photonic circuits on the surface of a chip. Today, most of these circuits are designed for a specific application, but the increase in complexity has introduced a generation of photonic circuits that can be programmed using software for a wide variety of functions through a mesh of on-chip waveguides, tunable beam couplers and optical phase shifters. Here we discuss the state of this emerging technology, including recent developments in photonic building blocks and circuit architectures, as well as electronic control and programming strategies. We cover possible applications in linear matrix operations, quantum information processing and microwave photonics, and examine how these generic chips can accelerate the development of future photonic circuits by providing a higher-level platform for prototyping novel optical functionalities without the need for custom chip fabrication.

Hartree-Fock on a superconducting qubit quantum computer

The simulation of fermionic systems is among the most anticipated applications of quantum computing. We performed several quantum simulations of chemistry with up to one dozen qubits, including modeling the isomerization mechanism of diazene. We also demonstrated error-mitigation strategies based on N-representability that dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realized the Givens rotation approach to noninteracting fermion evolution, which we variationally optimized to prepare the Hartree-Fock wave function. This ubiquitous algorithmic primitive is classically tractable to simulate yet still generates highly entangled states over the computational basis, which allowed us to assess the performance of our hardware and establish a foundation for scaling up correlated quantum chemistry simulations.

Demonstration of chip-based coupled degenerate optical parametric oscillators for realizing a nanophotonic spin-glass

The need for solving optimization problems is prevalent in various physical applications, including neuroscience, network design, biological systems, socio-economics, and chemical reactions. Many of these are classified as non-deterministic polynomial-time hard and thus become intractable to solve as the system scales to a large number of elements. Recent research advances in photonics have sparked interest in using a network of coupled degenerate optical parametric oscillators (DOPOs) to effectively find the ground state of the Ising Hamiltonian, which can be used to solve other combinatorial optimization problems through polynomial-time mapping. Here, using the nanophotonic silicon-nitride platform, we demonstrate a spatial-multiplexed DOPO system using continuous-wave pumping. We experimentally demonstrate the generation and coupling of two microresonator-based DOPOs on a single chip. Through a reconfigurable phase link, we achieve both in-phase and out-of-phase operation, which can be deterministically achieved at a fast regeneration speed of 400 kHz with a large phase tolerance.

Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement

An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et al., Nature Physics (2018), 14, 1032–1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.

The diamond mesh, a phase-error- and loss-tolerant field-programmable MZI-based optical processor for optical neural networks

This paper presents the performance analysis of a phase error- and loss-tolerant multiport field-programmable MZI-based structure for optical neural networks (ONNs). Compared to the triangular (Reck) mesh, our proposed diamond mesh makes use of a larger number of MZIs, leading to a symmetric topology and adding additional degrees of freedom for the weight matrix optimization in the backpropagation process. Furthermore, the additional MZIs enable the diamond mesh to optimally eliminate the excess light intensity that degrades the performance of the ONNs through the tapered out waveguides. Our results show that the diamond topology is more robust to the inevitable imperfections in practice, i.e., insertion loss of the constituent MZIs and the phase errors. This robustness allows for better classification accuracy in the presence of experimental imperfections. The practical performance and the scalability of the two structures implementing different sizes of optical neural networks are analytically compared. The obtained results confirm that the diamond mesh is more error- and loss-tolerant in classifying the data samples in different sizes of ONNs.

Computer-Inspired Concept for High-Dimensional Multipartite Quantum Gates

An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multiphotonic quantum systems. The proposals rely on two new ideas: (i) a novel high-dimensional quantum nondemolition measurement, (ii) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world and thereby we identify important pathways for experimental research in the near future. The concepts have been found using the computer algorithm melvin for designing computer-inspired quantum experiments. As opposed to the field of machine learning, here the human learns new scientific concepts by interpreting and analyzing the results presented by the machine. This demonstrates that computer algorithms can inspire new ideas in science, which has a widely unexplored potential that goes far beyond experimental quantum information science.

Computer-Inspired Concept for High-Dimensional Multipartite Quantum Gates

An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multiphotonic quantum systems. The proposals rely on two new ideas: (i) a novel high-dimensional quantum nondemolition measurement, (ii) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world and thereby we identify important pathways for experimental research in the near future. The concepts have been found using the computer algorithm melvin for designing computer-inspired quantum experiments. As opposed to the field of machine learning, here the human learns new scientific concepts by interpreting and analyzing the results presented by the machine. This demonstrates that computer algorithms can inspire new ideas in science, which has a widely unexplored potential that goes far beyond experimental quantum information science.

Efficient all-optical router and beam splitter for light with orbital angular momentum

We propose an efficient scheme for realizing all-optical router or beam splitter (BS) by employing a double tripod-type atomic system, where the ground levels are coupled by two additional intensity-dependent weak microwave fields. We show that the high-dimensional probe field encoded in a degree of freedom of orbital angular momentum can be stored, retrieved, and manipulated. Due to the constructive or destructive interference between the introduced microwave fields and the atomic spin coherence, the generated stationary light pulses and the retrieved probe fields can be increased or decreased with high efficiency and fidelity in a controllable manner. On the basis of the results and a general extension, a tunable all-optical router or BS, which can split a high-dimensional probe field into two or more ones, can be achieved by actively operating the controlling fields and the microwave fields. The current scheme, integrating multiple functions and showing excellent performance, could greatly enhance the tunability and capacity for the all-optical information processing.

Silicon erasable waveguides and directional couplers by germanium ion implantation for configurable photonic circuits

A novel technique for realization of configurable/one-time programmable (OTP) silicon photonic circuits is presented. Once the proposed photonic circuit is programmed, its signal routing is retained without the need for additional power consumption. This technology can potentially enable a multi-purpose design of photonic chips for a range of different applications and performance requirements, as it can be programmed for each specific application after chip fabrication. Therefore, the production costs per chip can be reduced because of the increase in production volume, and rapid prototyping of new photonic circuits is enabled. Essential building blocks for the configurable circuits in the form of erasable directional couplers (DCs) were designed and fabricated, using ion implanted waveguides. We demonstrate permanent switching of optical signals between the drop port and through the port of the DCs using a localized post-fabrication laser annealing process. Proof-of-principle demonstrators in the form of generic 1×4 and 2×2 programmable switching circuits were fabricated and subsequently programmed.

Phase estimation algorithm for the multibeam optical metrology

Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can be translated into the classical linear optical framework. The developed setup made of beam splitters, mirrors and phase shifters demonstrates how the classical coherence, similarly to the quantum coherence, poses a resource for obtaining information about the measurable physical quantities. Our study opens route to the reliable implementation of the small-scale unitary algorithms on path-encoded qudits, thus establishing an easily accessible platform for unitary computation.

High-Dimensional Frequency-Encoded Quantum Information Processing with Passive Photonics and Time-Resolving Detection

In this Letter, we propose a new approach to process high-dimensional quantum information encoded in a photon frequency domain. In contrast to previous approaches based on nonlinear optical processes, no active control of photon energy is required. Arbitrary unitary transformation and projection measurement can be realized with passive photonic circuits and time-resolving detection. A systematic circuit design for a quantum frequency comb with arbitrary size has been given. The criteria to verify quantum frequency correlation has been derived. By considering the practical condition of the detector's finite response time, we show that high-fidelity operation can be readily realized with current device performance. This work will pave the way towards scalable and high-fidelity quantum information processing based on high-dimensional frequency encoding.

Optimal design of error-tolerant reprogrammable multiport interferometers

Photonic information processing demands programmable multiport interferometers capable of implementing arbitrary transfer matrices, for which planar meshes of error-sensitive Mach-Zehnder interferometers are usually exploited. We propose an alternative design that uses a single-static beam splitter (BS) and a variable phase shift as the building blocks. The design possesses superior resilience to manufacturing errors and losses without extra elements added into the scheme. Namely, the power transmissivities of the static BSs can take arbitrary values in the range from ≈1/2 to ≈4/5. In this Letter, we show that the fraction of transfer matrices non-implementable by the interferometers of our design diminishes rapidly with its size.

Negativity of Quasiprobability Distributions as a Measure of Nonclassicality

We demonstrate that the negative volume of any s-parametrized quasiprobability, including the Glauber-Sudashan P function, can be consistently defined and forms a continuous hierarchy of nonclassicality measures that are linear optical monotones. These measures belong to an operational resource theory of nonclassicality based on linear optical operations. The negativity of the Glauber-Sudashan P function, in particular, can be shown to have an operational interpretation as the robustness of nonclassicality. We then introduce an approximate linear optical monotone, and we show that this nonclassicality quantifier is computable and is able to identify the nonclassicality of nearly all nonclassical states.

Regimes of Classical Simulability for Noisy Gaussian Boson Sampling

As a promising candidate for exhibiting quantum computational supremacy, Gaussian boson sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS-in the form of an inequality between the input squeezing parameter, the overall transmission rate, and the quality of photon detectors. Our result serves as a nonclassicality test that must be passed by any quantum computational supremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.

Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry

We solve the general problem of determining, through imaging, the three-dimensional positions of N weak incoherent pointlike emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a passive linear interferometer feeds into an array of photodetectors is always optimal for this estimation problem, in the sense that it saturates the quantum Cramér-Rao bound. We provide a method for the explicit construction of the optimal interferometer. Further explicit results for the quantum Fisher information and the optimal interferometer design that attains it are obtained for the special case of one and two incoherent emitters in the paraxial regime. This work provides insights into the phenomenon of superresolution through incoherent imaging that has attracted much attention recently. Our results will find a wide range of applications over a broad spectrum of frequencies, from fluorescence microscopy to stellar interferometry.

A quantum algorithm for evolving open quantum dynamics on quantum computing devices

Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.

Heuristic recurrent algorithms for photonic Ising machines

The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort toward developing application-specific hardware across many different fields of engineering, such as integrated circuits, memristors, and photonics. However, unleashing the potential of such architectures requires the development of algorithms which optimally exploit their fundamental properties. Here, we present the Photonic Recurrent Ising Sampler (PRIS), a heuristic method tailored for parallel architectures allowing fast and efficient sampling from distributions of arbitrary Ising problems. Since the PRIS relies on vector-to-fixed matrix multiplications, we suggest the implementation of the PRIS in photonic parallel networks, which realize these operations at an unprecedented speed. The PRIS provides sample solutions to the ground state of Ising models, by converging in probability to their associated Gibbs distribution. The PRIS also relies on intrinsic dynamic noise and eigenvalue dropout to find ground states more efficiently. Our work suggests speedups in heuristic methods via photonic implementations of the PRIS.

Robust Architecture for Programmable Universal Unitaries

The decomposition of large unitary matrices into smaller ones is important because it provides ways to the realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel blocks; however, the schemes turn out to be sensitive to fabrication errors. We study a novel decomposition method based on multichannel blocks. We have shown that the scheme is universal even when the block's transfer matrices are chosen at random, making it virtually insensitive to errors. Moreover, the placement of the variable elements can be arbitrary, so that the scheme is not bound to specific topologies. Our method can be beneficial for large-scale implementations of unitary transformations by techniques, which are not of wide proliferation today or have yet to be developed.

Entangling three qubits without ever touching

All identical particles are inherently correlated from the outset, regardless of how far apart their creation took place. In this paper, this fact is used for extraction of entanglement from independent particles unaffected by any interactions. Specifically, we are concerned with operational schemes for generation of all tripartite entangled states, essentially the GHZ state and the W state, which prevent the particles from touching one another over the entire evolution. The protocols discussed in the paper require only three particles in linear optical setups with equal efficiency for boson, fermion or anyon statistics. Within this framework indistinguishability of particles presents itself as a useful resource of entanglement accessible for practical applications.

Efficient training and design of photonic neural network through neuroevolution

Recently, optical neural networks (ONNs) integrated into photonic chips have received extensive attention because they are expected to implement the same pattern recognition tasks in electronic platforms with high efficiency and low power consumption. However, there are no efficient learning algorithms for the training of ONNs on an on-chip integration system. In this article, we propose a novel learning strategy based on neuroevolution to design and train ONNs. Two typical neuroevolution algorithms are used to determine the hyper-parameters of ONNs and to optimize the weights (phase shifters) in the connections. To demonstrate the effectiveness of the training algorithms, the trained ONNs are applied in classification tasks for an iris plants dataset, a wine recognition dataset and modulation formats recognition. The calculated results demonstrate that the accuracy and stability of the training algorithms based on neuroevolution are competitive with other traditional learning algorithms. In comparison to previous works, we introduce an efficient training method for ONNs and demonstrate their broad application prospects in pattern recognition, reinforcement learning and so on.

Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a 10^{14}-Dimensional Hilbert Space

Quantum computing experiments are moving into a new realm of increasing size and complexity, with the short-term goal of demonstrating an advantage over classical computers. Boson sampling is a promising platform for such a goal; however, the number of detected single photons is up to five so far, limiting these small-scale implementations to a proof-of-principle stage. Here, we develop solid-state sources of highly efficient, pure, and indistinguishable single photons and 3D integration of ultralow-loss optical circuits. We perform experiments with 20 pure single photons fed into a 60-mode interferometer. In the output, we detect up to 14 photons and sample over Hilbert spaces with a size up to 3.7×10^{14}, over 10 orders of magnitude larger than all previous experiments, which for the first time enters into a genuine sampling regime where it becomes impossible to exhaust all possible output combinations. The results are validated against distinguishable samplers and uniform samplers with a confidence level of 99.9%.

Ultrasmall design of a universal linear circuit based on microring resonators

We designed a universal linear circuit by using microring resonators instead of conventional Mach-Zehnder interferometers and phase shifters. We illustrated that the footprint of the universal linear circuit can be drastically reduced (∼ 1/10). In addition, power consumption can also be reduced by using the sensitivity of the phase change in the vicinity of the resonant peak. Furthermore, as an important example of the application for optical communication, MIMO compensation operation is numerically demonstrated by our proposed universal linear circuit. The proposed design can be adapted to other experimentally reported devices, which will accelerate the integration of the universal linear circuit.

Ptychography of pure quantum states

Ptychography is an imaging technique in which a localized illumination scans overlapping regions of an object and generates a set of diffraction intensities used to computationally reconstruct its complex-valued transmission function. We propose a quantum analogue of this technique designed to reconstruct d-dimensional pure states. A set of n rank-r projectors “scans” overlapping parts of an input state and the moduli of the d Fourier amplitudes of each part are measured. These nd outcomes are fed into an iterative phase retrieval algorithm that estimates the state. Using d up to 100 and r around d / 2, we performed numerical simulations for single systems in an economic (n = 4) and a costly (n = d) scenario, as well as for multiqubit systems (n = 6logd). This numeric study included realistic amounts of depolarization and poissonian noise, and all scenarios yielded, in general, reconstructions with infidelities below 10⁻². The method is shown, therefore, to be resilient to noise and, for any d, requires a simple and fast postprocessing algorithm. We show that the algorithm is equivalent to an alternating gradient search, which ensures that it does not suffer from local-minima stagnation. Unlike traditional approaches to state reconstruction, the ptychographic scheme uses a single measurement basis; the diversity and redundancy in the measured data—key for its success—are provided by the overlapping projections. We illustrate the simplicity of this scheme with the paradigmatic multiport interferometer.

Sorting-based approach to multiphoton interference

Multiphoton interference is an essential component of quantum technologies such as quantum computation, quantum communication, and quantum metrology. We introduce a sorting-based approach to multiphoton interference and examine its implications for quantum metrology and teleportation. Our examination reveals an extension of the seminal Hong-Ou-Mandel effect whose resultant state is the highly desired multiphoton NOON state. Application of the above perspective to entangled photons reveals a novel approach to quantum qudit teleportation.

Programmable SCOW Mesh Silicon Photonic Processor for Linear Unitary Operator

Universal unitary multiport interferometers (UMIs) can perform any arbitrary unitary transformation to a vector of input optical modes, which are essential for a wide range of applications. Most UMIs are realized by fixed photonic circuits with a triangular or a rectangular architecture. Here, we present the implementation of an N × N rectangular UMI with a programmable photonic processor based on two-dimensional meshes of self-coupled optical waveguide (SCOW) resonant structures. Our architecture shows a high tolerance to the unbalanced loss upon interference. This work enriches the functionality of the SCOW mesh photonic processors, which are promising for field-programmable photonic arrays.

8×8 reconfigurable quantum photonic processor based on silicon nitride waveguides

The development of large-scale optical quantum information processing circuits ground on the stability and reconfigurability enabled by integrated photonics. We demonstrate a reconfigurable 8×8 integrated linear optical network based on silicon nitride waveguides for quantum information processing. Our processor implements a novel optical architecture enabling any arbitrary linear transformation and constitutes the largest programmable circuit reported so far on this platform. We validate a variety of photonic quantum information processing primitives, in the form of Hong-Ou-Mandel interference, bosonic coalescence/anti-coalescence and high-dimensional single-photon quantum gates. We achieve fidelities that clearly demonstrate the promising future for large-scale photonic quantum information processing using low-loss silicon nitride.

Efficient hyperentanglement purification for three-photon systems with the fidelity-robust quantum gates and hyperentanglement link

We present an efficient and faithful hyperentanglement purification protocol (hyper-EPP) for three-photon system in mixed hyperentangled Greenberger-Horne-Zeilinger states with bit-flip errors in both spatial-mode and polarization degrees of freedom (DOFs), resorting to the fidelity-robust quantum gates and hyperentanglement link. Our high-efficiency hyper-EPP comes from two aspects. One is to pump the higher-fidelity hyperentanglement from different three-photon systems into the same three-photon system with fidelity-robust swap gates, the other is to reproduce some hyperentangled three-photon systems from hyperentangled two-photon subsystems based on hyperentanglement link. Moreover, as the infidelity originating from imperfect single-photon scattering can be heralded as a failure by triggering a detector, our hyper-EPP operates faithfully with the present quantum circuits. Furthermore, our hyper-EPP can be directly extended to purify multiple photon systems entangled in one DOF or hyperentangled in multiple DOFs.

Directionally-Unbiased Unitary Optical Devices in Discrete-Time Quantum Walks

The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call “directionally-biased”. Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recently to eliminate the directional bias, greatly reducing the numbers of required beam splitters when implementing complicated tasks. Analysis of some originally directional optical devices and basic principles of their conversion into directionally-unbiased systems form the base of this paper. Photonic quantum walk implementations are investigated as a main application of the use of directionally-unbiased systems. Several quantum walk procedures executed on graph networks constructed using directionally-unbiased nodes are discussed. A significant savings in hardware and other required resources when compared with traditional directionally-biased beam-splitter-based optical networks is demonstrated.

Quantum Teleportation in High Dimensions

Quantum teleportation allows a "disembodied" transmission of unknown quantum states between distant quantum systems. Yet, all teleportation experiments to date were limited to a two-dimensional subspace of quantized multiple levels of the quantum systems. Here, we propose a scheme for teleportation of arbitrarily high-dimensional photonic quantum states and demonstrate an example of teleporting a qutrit. Measurements over a complete set of 12 qutrit states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), which is well above both the optimal single-copy qutrit state-estimation limit of 1/2 and maximal qubit-qutrit overlap of 2/3, thus confirming a genuine and nonclassical three-dimensional teleportation. Our work will enable advanced quantum technologies in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.

Hyperparallel transistor, router and dynamic random access memory with unity fidelities

We theoretically implement some hyperparallel optical elements, including quantum single photon transistor, router, and dynamic random access memory (DRAM). The inevitable side leakage and the imperfect birefringence of the quantum dot (QD)-cavity mediates are taken into account, and unity fidelities of our optical elements can be achieved. The hyperparallel constructions are based on polarization and spatial degrees of freedom (DOFs) of the photon to increase the parallel efficiency, improve the capacity of channel, save the quantum resources, reduce the operation time, and decrease the environment noises. Moreover, the practical schemes are robust against the side leakage and the coupling strength limitation in the microcavities.

Universal bound on sampling bosons in linear optics and its computational implications

In linear optics, photons are scattered in a network through passive optical elements including beam splitters and phase shifters, leading to many intriguing applications in physics, such as Mach-Zehnder interferometry, the Hong-Ou-Mandel effect, and tests of fundamental quantum mechanics. Here we present the fundamental limit in the transition amplitudes of bosons, applicable to all physical linear optical networks. Apart from boson sampling, this transition bound results in many other interesting applications, including behaviors of Bose-Einstein condensates (BEC) in optical networks, counterparts of Hong-Ou-Mandel effects for multiple photons, and approximating permanents of matrices. In addition, this general bound implies the existence of a polynomial-time randomized algorithm for estimating the transition amplitudes of bosons, which represents a solution to an open problem raised by Aaronson and Hance (Quantum Inf Comput 2012; 14: 541-59). Consequently, this bound implies that computational decision problems encoded in linear optics, prepared and detected in the Fock basis, can be solved efficiently by classical computers within additive errors. Furthermore, our result also leads to a classical sampling algorithm that can be applied to calculate the many-body wave functions and the S-matrix of bosonic particles.

Design of optical neural networks with component imprecisions

For the benefit of designing scalable, fault resistant optical neural networks (ONNs), we investigate the effects architectural designs have on the ONNs' robustness to imprecise components. We train two ONNs - one with a more tunable design (GridNet) and one with better fault tolerance (FFTNet) - to classify handwritten digits. When simulated without any imperfections, GridNet yields a better accuracy (∼98%) than FFTNet (∼95%). However, under a small amount of error in their photonic components, the more fault tolerant FFTNet overtakes GridNet. We further provide thorough quantitative and qualitative analyses of ONNs' sensitivity to varying levels and types of imprecisions. Our results offer guidelines for the principled design of fault-tolerant ONNs as well as a foundation for further research.

Asymmetrical hyperentanglement concentration for entanglement of polarization and orbital angular momentum

We propose two hyperentanglement concentration protocols (hyper-ECPs) for two-photon entangled states in the polarization and orbital angular momentum degrees of freedom. The two cases distilling a maximally hyperentangled state from partially entangled pure state with unknown parameters and known parameters are dissected respectively. Both of the protocols require only linear optical elements which make our protocols more feasible for current technologies. In our protocols, the remote parties perform different local operations, which will reduce everyone's operation and improve the total efficiency. Each of them has the theoretical maximum success probability in the corresponding situation. The hyper-ECPs can be exploited simply to hyperentangled Greenberger-Horne-Zeilinger states.

Cyclic permutations for qudits in d dimensions

One of the main challenges in quantum technologies is the ability to control individual quantum systems. This task becomes increasingly difficult as the dimension of the system grows. Here we propose a general setup for cyclic permutations Xd in d dimensions, a major primitive for constructing arbitrary qudit gates. Using orbital angular momentum states as a qudit, the simplest implementation of the Xd gate in d dimensions requires a single quantum sorter Sd and two spiral phase plates. We then extend this construction to a generalised Xd(p) gate to perform a cyclic permutation of a set of d, equally spaced values {|[Formula: see text]〉, |[Formula: see text] + p〉, …, |[Formula: see text] + (d - 1)p〉} [Formula: see text] {|[Formula: see text] + p〉, |[Formula: see text] + 2p〉, …, |[Formula: see text]〉}. We find compact implementations for the generalised Xd(p) gate in both Michelson (one sorter Sd, two spiral phase plates) and Mach-Zehnder configurations (two sorters Sd, two spiral phase plates). Remarkably, the number of spiral phase plates is independent of the qudit dimension d. Our architecture for Xd and generalised Xd(p) gate will enable complex quantum algorithms for qudits, for example quantum protocols using photonic OAM states.

Highly parallel simulation and optimization of photonic circuits in time and frequency domain based on the deep-learning framework PyTorch

We propose a new method for performing photonic circuit simulations based on the scatter matrix formalism. We leverage the popular deep-learning framework PyTorch to reimagine photonic circuits as sparsely connected complex-valued neural networks. This allows for highly parallel simulation of large photonic circuits on graphical processing units in time and frequency domain while all parameters of each individual component can easily be optimized with well-established machine learning algorithms such as backpropagation.

Percolation thresholds for photonic quantum computing

Despite linear-optical fusion (Bell measurement) being probabilistic, photonic cluster states for universal quantum computation can be prepared without feed-forward by fusing small n-photon entangled clusters, if the success probability of each fusion attempt is above a threshold, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{\lambda }}_{\mathrm{c}}^{(n)}$$\end{document}λc(n). We prove a general bound \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{\lambda }}_{\mathrm{c}}^{(n)} \ge 1/(n - 1)$$\end{document}λc(n)≥1∕(n-1), and develop a conceptual method to construct long-range-connected clusters where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{\lambda }}_{\mathrm{c}}^{(n)}$$\end{document}λc(n) becomes the bond percolation threshold of a logical graph. This mapping lets us find constructions that require lower fusion success probabilities than currently known, and settle a heretofore open question by showing that a universal cluster state can be created by fusing 3-photon clusters over a 2D lattice with a fusion success probability that is achievable with linear optics and single photons, making this attractive for integrated-photonic realizations.

Universal cluster states for quantum computing can be assembled without feed-forward by fusing n-photon clusters with linear optics if the fusion success probability is above a threshold p. The authors bound p in terms of n and provide protocols for n = 3 clusters requiring lower fusion probability than before.

Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale

Nanophotonics has been an active research field over the past two decades, triggered by the rising interests in exploring new physics and technologies with light at the nanoscale. As the demands of performance and integration level keep increasing, the design and optimization of nanophotonic devices become computationally expensive and time-inefficient. Advanced computational methods and artificial intelligence, especially its subfield of machine learning, have led to revolutionary development in many applications, such as web searches, computer vision, and speech/image recognition. The complex models and algorithms help to exploit the enormous parameter space in a highly efficient way. In this review, we summarize the recent advances on the emerging field where nanophotonics and machine learning blend. We provide an overview of different computational methods, with the focus on deep learning, for the nanophotonic inverse design. The implementation of deep neural networks with photonic platforms is also discussed. This review aims at sketching an illustration of the nanophotonic design with machine learning and giving a perspective on the future tasks.