Experimental realization of any discrete unitary operator

Architecture agnostic algorithm for reconfigurable optical interferometer programming

We develop the learning algorithm to build an architecture agnostic model of a reconfigurable optical interferometer. A procedure of programming a unitary transformation of optical modes of an interferometer either follows an analytical expression yielding a unitary matrix given a set of phase shifts or requires an optimization routine if an analytic decomposition does not exist. Our algorithm adopts a supervised learning strategy which matches a model of an interferometer to a training set populated by samples produced by a device under study. A simple optimization routine uses the trained model to output phase shifts corresponding to a desired unitary transformation of the interferometer with a given architecture. Our result provides the recipe for efficient tuning of interferometers even without rigorous analytical description which opens opportunity to explore new architectures of the interferometric circuits.

Universal linear optics by programmable multimode interference

We introduce a constructive algorithm for universal linear electromagnetic transformations between the N input and N output modes of a dielectric slab. The approach uses out-of-plane phase modulation programmed down to N² degrees of freedom. The total area of these modulators equals that of the entire slab: our scheme makes optimal use of the available area for optical modulation. We also present error correction schemes that enable high-fidelity unitary transformations at large N. This "programmable multimode interferometer" (ProMMI) thus translates the algorithmic simplicity of Mach-Zehnder meshes into a holographically programmed slab, yielding DoF-limited compactness and error tolerance while eliminating the dominant sidewall-related optical losses and directional-coupler-related patterning challenges.

All-optical synthesis of an arbitrary linear transformation using diffractive surfaces

Spatially-engineered diffractive surfaces have emerged as a powerful framework to control light-matter interactions for statistical inference and the design of task-specific optical components. Here, we report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (N_i) and output (N_o), where N_i and N_o represent the number of pixels at the input and output fields-of-view (FOVs), respectively. First, we consider a single diffractive surface and use a matrix pseudoinverse-based method to determine the complex-valued transmission coefficients of the diffractive features/neurons to all-optically perform a desired/target linear transformation. In addition to this data-free design approach, we also consider a deep learning-based design method to optimize the transmission coefficients of diffractive surfaces by using examples of input/output fields corresponding to the target transformation. We compared the all-optical transformation errors and diffraction efficiencies achieved using data-free designs as well as data-driven (deep learning-based) diffractive designs to all-optically perform (i) arbitrarily-chosen complex-valued transformations including unitary, nonunitary, and noninvertible transforms, (ii) 2D discrete Fourier transformation, (iii) arbitrary 2D permutation operations, and (iv) high-pass filtered coherent imaging. Our analyses reveal that if the total number (N) of spatially-engineered diffractive features/neurons is ≥N_i × N_o, both design methods succeed in all-optical implementation of the target transformation, achieving negligible error. However, compared to data-free designs, deep learning-based diffractive designs are found to achieve significantly larger diffraction efficiencies for a given N and their all-optical transformations are more accurate for N < N_i × N_o. These conclusions are generally applicable to various optical processors that employ spatially-engineered diffractive surfaces.

Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology

The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits trade-offs in the precision with which each parameter can be estimated. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix as the metric tensor linked to the geometry of the underlying algebra su(n), with applications in numerous fields. This ensures an intrinsic bound that is independent of the choice of parametrization.

Implementation of a 3 × 3 directionally-unbiased linear optical multiport

Linear optical multiports are widely used in photonic quantum information processing. Naturally, these devices are directionally-biased since photons always propagate from the input ports toward the output ports. Recently, the concept of directionally-unbiased linear optical multiports was proposed. These directionally-unbiased multiports allow photons to propagate along a reverse direction, which can greatly reduce the number of required linear optical elements for complicated linear optical quantum networks. Here, we report an experimental demonstration of a 3 × 3 directionally-unbiased linear optical fiber multiport using an optical tritter and mirrors. Compared to the previous demonstration using bulk optical elements which works only with light sources with a long coherence length, our experimental directionally-unbiased 3 × 3 optical multiport does not require a long coherence length since it provides negligible optical path length differences among all possible optical trajectories. It can be a useful building block for implementing large-scale quantum walks on complex graph networks.

Materials for emergent silicon-integrated optical computing

Progress in computing architectures is approaching a paradigm shift: traditional computing based on digital complementary metal-oxide semiconductor technology is nearing physical limits in terms of miniaturization, speed, and, especially, power consumption. Consequently, alternative approaches are under investigation. One of the most promising is based on a "brain-like" or neuromorphic computation scheme. Another approach is quantum computing using photons. Both of these approaches can be realized using silicon photonics, and at the heart of both technologies is an efficient, ultra-low power broad band optical modulator. As silicon modulators suffer from relatively high power consumption, materials other than silicon itself have to be considered for the modulator. In this Perspective, we present our view on such materials. We focus on oxides showing a strong linear electro-optic effect that can also be integrated with Si, thus capitalizing on new materials to enable the devices and circuit architectures that exploit shifting computational machine learning paradigms, while leveraging current manufacturing infrastructure. This is expected to result in a new generation of computers that consume less power and possess a larger bandwidth.

Quantum verification of NP problems with single photons and linear optics

Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the satisfiability of potentially conflict constraints (SAT). According to the well-founded exponential time hypothesis, verifying an SAT instance of size n requires generally the complete solution in an O(n)-bit proof. In contrast, quantum verification algorithms, which encode the solution into quantum bits rather than classical bit strings, can perform the verification task with quadratically reduced information about the solution in [Formula: see text] qubits. Here we realize the quantum verification machine of SAT with single photons and linear optics. By using tunable optical setups, we efficiently verify satisfiable and unsatisfiable SAT instances and achieve a clear completeness-soundness gap even in the presence of experimental imperfections. The protocol requires only unentangled photons, linear operations on multiple modes and at most two-photon joint measurements. These features make the protocol suitable for photonic realization and scalable to large problem sizes with the advances in high-dimensional quantum information manipulation and large scale linear-optical systems. Our results open an essentially new route toward quantum advantages and extend the computational capability of optical quantum computing.

Waveguide-lattice-based architecture for multichannel optical transformations

We consider waveguide lattices as the architecture to implement a wide range of multiport transformations. In this architecture, a particular transfer matrix is obtained by setting step-wise profiles of propagation constants experienced by a field evolving in a lattice. To investigate the capabilities of this architecture, we numerically study the implementation of random transfer matrices as well as several notable cases, such as the discrete Fourier transform, the Hadamard, and permutation matrices. We show that waveguide lattice schemes are more compact than their traditional lumped-parameter counterparts, thus the proposed architecture may be beneficial for photonic information processing systems of the future.

Photonic Integrated Reconfigurable Linear Processors as Neural Network Accelerators

Reconfigurable linear optical processors can be used to perform linear transformations and are instrumental in effectively computing matrix–vector multiplications required in each neural network layer. In this paper, we characterize and compare two thermally tuned photonic integrated processors realized in silicon-on-insulator and silicon nitride platforms suited for extracting feature maps in convolutional neural networks. The reduction in bit resolution when crossing the processor is mainly due to optical losses, in the range 2.3–3.3 for the silicon-on-insulator chip and in the range 1.3–2.4 for the silicon nitride chip. However, the lower extinction ratio of Mach–Zehnder elements in the latter platform limits their expressivity (i.e., the capacity to implement any transformation) to 75%, compared to 97% of the former. Finally, the silicon-on-insulator processor outperforms the silicon nitride one in terms of footprint and energy efficiency.

Photonic Matrix Computing: From Fundamentals to Applications

In emerging artificial intelligence applications, massive matrix operations require high computing speed and energy efficiency. Optical computing can realize high-speed parallel information processing with ultra-low energy consumption on photonic integrated platforms or in free space, which can well meet these domain-specific demands. In this review, we firstly introduce the principles of photonic matrix computing implemented by three mainstream schemes, and then review the research progress of optical neural networks (ONNs) based on photonic matrix computing. In addition, we discuss the advantages of optical computing architectures over electronic processors as well as current challenges of optical computing and highlight some promising prospects for the future development.

Key Technologies of Photonic Artificial Intelligence Chip Structure and Algorithm

Artificial intelligence chips (AICs) are the intersection of integrated circuits and artificial intelligence (AI), involving structure design, algorithm analysis, chip fabrication and application scenarios. Due to their excellent ability in data processing, AICs show a long-term industrial prospect in big data services, cloud centers, etc. However, with the conceivable exhaustion of Moore’s Law, the size of traditional electronic AICs (EAICs) is gradually approaching the limit, and an architectural update is highly required. Photonic artificial intelligence chips (PAIC) utilize light beam propagation in the silicon waveguide, contributing to a high parallelism configuration, fast calculation speed and low latency. Due to light manipulation, PAICs perform well in anti-electromagnetic interference and energy conservation. This invited paper summarized the recent research on PAICs. The characteristics of different hardware structures are discussed. The current widely used training algorithm is given and the Photonic Design Automatic (PDA) simulation platform is introduced. In addition, the authors’ related work on PAICs is presented and we believe that PAICs may play a critical role in the deployment of data processing technology.

Inverse Design for Silicon Photonics: From Iterative Optimization Algorithms to Deep Neural Networks

Silicon photonics is a low-cost and versatile platform for various applications. For design of silicon photonic devices, the light-material interaction within its complex subwavelength geometry is difficult to investigate analytically and therefore numerical simulations are majorly adopted. To make the design process more time-efficient and to improve the device performance to its physical limits, various methods have been proposed over the past few years to manipulate the geometries of silicon platform for specific applications. In this review paper, we summarize the design methodologies for silicon photonics including iterative optimization algorithms and deep neural networks. In case of iterative optimization methods, we discuss them in different scenarios in the sequence of increased degrees of freedom: empirical structure, QR-code like structure and irregular structure. We also review inverse design approaches assisted by deep neural networks, which generate multiple devices with similar structure much faster than iterative optimization methods and are thus suitable in situations where piles of optical components are needed. Finally, the applications of inverse design methodology in optical neural networks are also discussed. This review intends to provide the readers with the suggestion for the most suitable design methodology for a specific scenario.

Arbitrary linear transformations for photons in the frequency synthetic dimension

Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a photonic architecture to achieve arbitrary linear transformations by harnessing the synthetic frequency dimension of photons. Our structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes carried by a single waveguide. By inverse design of these short- and long-range couplings using automatic differentiation, we realize arbitrary scattering matrices in synthetic space between the input and output frequency modes with near-unity fidelity and favorable scaling. We show that the same physical structure can be reconfigured to implement a wide variety of manipulations including single-frequency conversion, nonreciprocal frequency translations, and unitary as well as non-unitary transformations. Our approach enables compact, scalable and reconfigurable integrated photonic architectures to achieve arbitrary linear transformations in both the classical and quantum domains using current state-of-the-art technology.

Silicon nitride programmable photonic processor with folded heaters

General-purpose programmable photonic processors rely on the large-scale integration of beamsplitters and reconfigurable phase shifters, distributed within unit cells or photonic gates. With their future evolution threatened by several hardware constrains, including the integration density that can be achieved with current mesh topologies, in this work, we present a unit cell topology design to increase the integration density of waveguide mesh arrangements based on folded Mach-Zehnder Interferometers. We report the design details of a 40-unit cell waveguide mesh integrated in a 11mm x 5.5 mm silicon nitride chip achieving, to the best of our knowledge, the highest integration density reported to date for a general-purpose photonic processor. The chip is electrically interfaced to a PCB and we report examples of reconfigurable optical beamsplitters, basic tunable microwave photonic filters with high peak rejection (40 dB approx.), as well as the dynamic interconnection and routing of 5G digitally modulated signals within the photonic mesh.

Nanoprinted high-neuron-density optical linear perceptrons performing near-infrared inference on a CMOS chip

Optical machine learning has emerged as an important research area that, by leveraging the advantages inherent to optical signals, such as parallelism and high speed, paves the way for a future where optical hardware can process data at the speed of light. In this work, we present such optical devices for data processing in the form of single-layer nanoscale holographic perceptrons trained to perform optical inference tasks. We experimentally show the functionality of these passive optical devices in the example of decryptors trained to perform optical inference of single or whole classes of keys through symmetric and asymmetric decryption. The decryptors, designed for operation in the near-infrared region, are nanoprinted on complementary metal-oxide-semiconductor chips by galvo-dithered two-photon nanolithography with axial nanostepping of 10 nm1,2, achieving a neuron density of >500 million neurons per square centimetre. This power-efficient commixture of machine learning and on-chip integration may have a transformative impact on optical decryption3, sensing4, medical diagnostics5 and computing6,7.

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%.