Experimental realization of any discrete unitary operator

Information processing at the speed of light

In recent years, quantum computing has made significant strides, particularly in light-based technology. The introduction of quantum photonic chips has ushered in an era marked by scalability, stability, and cost-effectiveness, paving the way for innovative possibilities within compact footprints. This article provides a comprehensive exploration of photonic quantum computing, covering key aspects such as encoding information in photons, the merits of photonic qubits, and essential photonic device components including light squeezers, quantum light sources, interferometers, photodetectors, and waveguides. The article also examines photonic quantum communication and internet, and its implications for secure systems, detailing implementations such as quantum key distribution and long-distance communication. Emerging trends in quantum communication and essential reconfigurable elements for advancing photonic quantum internet are discussed. The review further navigates the path towards establishing scalable and fault-tolerant photonic quantum computers, highlighting quantum computational advantages achieved using photons. Additionally, the discussion extends to programmable photonic circuits, integrated photonics and transformative applications. Lastly, the review addresses prospects, implications, and challenges in photonic quantum computing, offering valuable insights into current advancements and promising future directions in this technology.

Measuring, processing, and generating partially coherent light with self-configuring optics

Optical phenomena always display some degree of partial coherence between their respective degrees of freedom. Partial coherence is of particular interest in multimodal systems, where classical and quantum correlations between spatial, polarization, and spectral degrees of freedom can lead to fascinating phenomena (e.g., entanglement) and be leveraged for advanced imaging and sensing modalities (e.g., in hyperspectral, polarization, and ghost imaging). Here, we present a universal method to analyze, process, and generate spatially partially coherent light in multimode systems by using self-configuring optical networks. Our method relies on cascaded self-configuring layers whose average power outputs are sequentially optimized. Once optimized, the network separates the input light into its mutually incoherent components, which is formally equivalent to a diagonalization of the input density matrix. We illustrate our method with numerical simulations of Mach-Zehnder interferometer arrays and show how this method can be used to perform partially coherent environmental light sensing, generation of multimode partially coherent light with arbitrary coherency matrices, and unscrambling of quantum optical mixtures. We provide guidelines for the experimental realization of this method, including the influence of losses, paving the way for self-configuring photonic devices that can automatically learn optimal modal representations of partially coherent light fields.

Optical neural networks: progress and challenges

Artificial intelligence has prevailed in all trades and professions due to the assistance of big data resources, advanced algorithms, and high-performance electronic hardware. However, conventional computing hardware is inefficient at implementing complex tasks, in large part because the memory and processor in its computing architecture are separated, performing insufficiently in computing speed and energy consumption. In recent years, optical neural networks (ONNs) have made a range of research progress in optical computing due to advantages such as sub-nanosecond latency, low heat dissipation, and high parallelism. ONNs are in prospect to provide support regarding computing speed and energy consumption for the further development of artificial intelligence with a novel computing paradigm. Herein, we first introduce the design method and principle of ONNs based on various optical elements. Then, we successively review the non-integrated ONNs consisting of volume optical components and the integrated ONNs composed of on-chip components. Finally, we summarize and discuss the computational density, nonlinearity, scalability, and practical applications of ONNs, and comment on the challenges and perspectives of the ONNs in the future development trends.

Orthogonal Thermal Noise and Transmission Signals: A New Coherent Perfect Absorption's Feature

Coherent perfect absorption (CPA) is an interference process associated with the zeros of the scattering matrix of interest for optical computing, data processing, and sensing. However, the noise properties of CPA remain relatively unexplored. Here, we demonstrate that CPA thermal noise signals exhibit a unique property: they are orthogonal to the signals transmitted through the network. In turn, such property enables a variety of thermal noise management effects, such as the physical separability of thermal noise and transmitted signals, and "externally lossless" networks that internally host radiative heat transfer processes. We believe that our results provide a new perspective on the many CPA technologies currently under development.

Programmable Photonic Quantum Circuits with Ultrafast Time-Bin Encoding

We propose a quantum information processing platform that utilizes the ultrafast time-bin encoding of photons. This approach offers a pathway to scalability by leveraging the inherent phase stability of collinear temporal interferometric networks at the femtosecond-to-picosecond timescale. The proposed architecture encodes information in ultrafast temporal bins processed using optically induced nonlinearities and birefringent materials while keeping photons in a single spatial mode. We demonstrate the potential for scalable photonic quantum information processing through two independent experiments that showcase the platform's programmability and scalability, respectively. The scheme's programmability is demonstrated in the first experiment, where we successfully program 362 different unitary transformations in up to eight dimensions in a temporal circuit. In the second experiment, we show the scalability of ultrafast time-bin encoding by building a passive optical network, with increasing circuit depth, of up to 36 optical modes. In each experiment, fidelities exceed 97%, while the interferometric phase remains passively stable for several days.

SU(N) symmetry of coherent photons controlled by rotated waveplates

The coherent state from a laser source has spin and orbital degrees of freedom, which allow an arbitrary superposition state among orthogonal states with varying amplitudes and phases. Here, we theoretically show coherent photons with SU(N) symmetry are characterised by expectation values of angular momentum shown on a hypersphere in SO(N 2 - 1 ) space. To demonstrate expected unitary transformations in experiments, we have constructed generators of transformations in the Lie group simply by combining widely available optical components such as waveplates and vortex lenses. We show a superposition state between twisted and Gaussian states is characterised by the dynamics of the topological charge upon the transformation in SU(3) states. We also realised photonic singlet and triplet states corresponding to SU(4) states, which were projected to SU(2)×SU(2) states upon passing through a rotated polariser.

Holographic Gaussian Boson Sampling with Matrix Product States on 3D cQED Processors

We introduce quantum circuits for simulations of multimode state vectors on 3D circuit quantum electrodynamics (cQED) processors using matrix product state representations. The circuits are demonstrated as applied to simulations of molecular docking based on holographic Gaussian boson sampling (GBS), as illustrated for the binding of a thiol-containing aryl sulfonamide ligand to the tumor necrosis factor-α converting enzyme receptor. We show that cQED devices with a modest number of modes could be employed to simulate multimode systems by repurposing working modes through measurement and reinitialization. We anticipate that a wide range of GBS applications could be implemented on compact 3D cQED processors analogously using the holographic approach. Simulations on qubit-based quantum computers could be implemented analogously using circuits that represent continuous variables in terms of truncated expansions of Fock states.

Direct electromagnetic information processing with planar diffractive neural network

Diffractive neural network in electromagnetic wave-driven system has attracted great attention due to its ultrahigh parallel computing capability and energy efficiency. However, recent neural networks based on the diffractive framework still face the bottlenecks of misalignment and relatively large size limiting their further applications. Here, we propose a planar diffractive neural network (pla-NN) with a highly integrated and conformal architecture to achieve direct signal processing in the microwave frequency. On the basis of printed circuit fabrication process, the misalignment could be effectively circumvented while enabling flexible extension for multiple conformal and stacking designs. We first conduct validation on the fashion-MNIST dataset and experimentally build up a system using the proposed network architecture for direct recognition of different geometry structures in the electromagnetic space. We envision that the presented architecture, once combined with the advanced dynamic maneuvering techniques and flexible topology, would exhibit unlimited potentials in the areas of high-performance computing, wireless sensing, and flexible wearable electronics.

Perfect linear optics using silicon photonics

Recently there has been growing interest in using photonics to perform the linear algebra operations of neuromorphic and quantum computing applications, aiming at harnessing silicon photonics' (SiPho) high-speed and energy-efficiency credentials. Accurately mapping, however, a matrix into optics remains challenging, since state-of-the-art optical architectures are sensitive to fabrication imperfections. This leads to reduced fidelity that degrades as the insertion losses of the optical matrix nodes or the matrix dimensions increase. In this work, we present the experimental deployment of a 4 × 4 coherent crossbar (Xbar) as a silicon chip and validate experimentally its theoretically predicted fidelity restoration credentials. We demonstrate the experimental implementation of 10,000 arbitrary linear transformations achieving a record-high fidelity of 99.997% ± 0.002, limited mainly by the measurement equipment. Our work represents an integrated optical circuit providing almost unity and loss-independent fidelity in the realization of arbitrary matrices, highlighting light's credentials in resolving complex computations.

Noncompletely Positive Quantum Maps Enable Efficient Local Energy Extraction in Batteries

Energy extraction from quantum batteries by means of completely positive trace-preserving (CPTP) maps leads to the concept of CPTP-local passive states, which identify bipartite states from which no energy can be squeezed out by applying any CPTP map to a particular subsystem. We prove, for arbitrary dimension, that if a state is CPTP-local passive with respect to a Hamiltonian, then an arbitrary number of copies of the same state-including an asymptotically large one-is also CPTP-local passive. We show further that energy can be extracted efficiently from CPTP-local passive states employing noncompletely positive trace-preserving (NCPTP) but still physically realizable maps on the same part of the shared battery on which operation of CPTP maps were useless. Moreover, we provide the maximum extractable energy using local-CPTP operations, and then, we present an explicit class of states and corresponding Hamiltonians, for which the maximum can be outperformed using physical local NCPTP maps. We provide a necessary and sufficient condition and a separate necessary condition for an arbitrary bipartite state to be unable to supply any energy using NCPTP operations on one party with respect to an arbitrary but fixed Hamiltonian. We build an analogy between the relative status of CPTP and NCPTP operations for energy extraction in quantum batteries, and the association of distillable entanglement with entanglement cost for asymptotic local manipulations of entanglement. The surpassing of the maximum energy extractable by NCPTP maps for CPTP-passive as well as for CPTP-nonpassive battery states can act as detectors of non-CPTPness of quantum maps.

Classical-Nonclassical Polarity of Gaussian States

Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multimode Gaussian states has posed some challenges. To address this, we introduce a unified quantification: the "classical-nonclassical polarity," represented by P. For a single mode, a positive value of P captures the reduced minimum quadrature uncertainty below the vacuum noise, while a negative value represents an enlarged uncertainty due to classical mixtures. For multimode systems, a positive P indicates bipartite quantum entanglement. We show that the sum of the total classical-nonclassical polarity is conserved under arbitrary linear optical transformations for any two-mode and three-mode Gaussian states. For any pure multimode Gaussian state, the total classical-nonclassical polarity equals the sum of the mean photon number from single-mode squeezing and two-mode squeezing. Our results provide a new perspective on the quantitative relation between single-mode nonclassicality and entanglement, which may find applications in a unified resource theory of nonclassical features.

Quantum Algorithm for Imaginary-Time Green's Functions

Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H2 and H4 on quantum simulators and on IBM's quantum devices.

Binary quantum random number generator based on value indefinite observables

All quantum random number generators based on measuring value indefinite observables are at least three-dimensional because the Kochen-Specker Theorem and the Located Kochen-Specker Theorem are false in dimension two. In this article, we construct quantum random number generators based on measuring a three-dimensional value indefinite observable that generates binary quantum random outputs with the same randomness qualities as the ternary ones: the outputs are maximally unpredictable.

Observation of Diverse Asymmetric Structures in High-Dimensional Einstein-Podolsky-Rosen Steering

Einstein-Podolsky-Rosen (EPR) steering, a distinctive quantum correlation, reveals a unique and inherent asymmetry. This research delves into the multifaceted asymmetry of EPR steering within high-dimensional quantum systems, exploring both theoretical frameworks and experimental validations. We introduce the concept of genuine high-dimensional one-way steering, wherein a high Schmidt number of bipartite quantum states is demonstrable in one steering direction but not reciprocally. Additionally, we explore two criteria to certify the lower and upper bounds of the Schmidt number within a one-sided device-independent context. These criteria serve as tools for identifying potential asymmetric dimensionality of EPR steering in both directions. By preparing two-qutrit mixed states with high fidelity, we experimentally observe asymmetric structures of EPR steering in the C^{3}⊗C^{3} Hilbert space. Our Letter offers new perspectives to understand the asymmetric EPR steering beyond qubits and has potential applications in asymmetric high-dimensional quantum information tasks.

The Goldilocks principle of learning unitaries by interlacing fixed operators with programmable phase shifters on a photonic chip

Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Programmable photonics provides a flexible platform that can be reconfigured to perform multiple tasks, thereby holding great promise for revolutionizing future optical networks and quantum computing systems. Over the past decade, there has been constant progress in developing several different architectures for realizing programmable photonic circuits that allow for realizing arbitrary discrete unitary operations with light. Here, we systematically investigate a general family of photonic circuits for realizing arbitrary unitaries based on a simple architecture that interlaces a fixed intervening layer with programmable phase shifter layers. We introduce a criterion for the intervening operator that guarantees the universality of this architecture for representing arbitrary N × N unitary operators with N + 1 phase layers. We explore this criterion for different photonic components, including photonic waveguide lattices and meshes of directional couplers, which allows the identification of several families of photonic components that can serve as the intervening layers in the interlacing architecture. Our findings pave the way for efficiently designing and realizing novel families of programmable photonic integrated circuits for multipurpose analog information processing.

Multiplexable all-optical nonlinear activator for optical computing

As an alternative solution to surpass electronic neural networks, optical neural networks (ONNs) offer significant advantages in terms of energy consumption and computing speed. Despite the optical hardware platform could provide an efficient approach to realizing neural network algorithms than traditional hardware, the lack of optical nonlinearity limits the development of ONNs. Here, we proposed and experimentally demonstrated an all-optical nonlinear activator based on the stimulated Brillouin scattering (SBS). Utilizing the exceptional carrier dynamics of SBS, our activator supports two types of nonlinear functions, saturable absorption and rectified linear unit (Relu) models. Moreover, the proposed activator exhibits large dynamic response bandwidth (∼11.24 GHz), low nonlinear threshold (∼2.29 mW), high stability, and wavelength division multiplexing identities. These features have potential advantages for the physical realization of optical nonlinearities. As a proof of concept, we verify the performance of the proposed activator as an ONN nonlinear mapping unit via numerical simulations. Simulation shows that our approach achieves comparable performance to the activation functions commonly used in computers. The proposed approach provides support for the realization of all-optical neural networks.

An atomic boson sampler

A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non-interacting dynamics1. An efficient exact classical simulation of boson sampling is not believed to exist, which has motivated ground-breaking boson sampling experiments in photonics with increasingly many photons2-12. However, it is difficult to generate and reliably evolve specific numbers of photons with low loss, and thus probabilistic techniques for postselection7 or marked changes to standard boson sampling10-12 are generally used. Here, we address the above challenges by implementing boson sampling using ultracold atoms13,14 in a two-dimensional, tunnel-coupled optical lattice. This demonstration is enabled by a previously unrealized combination of tools involving high-fidelity optical cooling and imaging of atoms in a lattice, as well as programmable control of those atoms using optical tweezers. When extended to interacting systems, our work demonstrates the core abilities required to directly assemble ground and excited states in simulations of various Hubbard models15,16.

On-chip photonic convolution by phase-change in-memory computing cells with quasi-continuous tuning

Matrix multiplication acceleration by on-chip photonic integrated circuits (PICs) is emerging as one of the attractive and promising solutions, offering outstanding benefits in speed and bandwidth as compared to non-photonic approaches. Incorporating nonvolatile phase-change materials into PICs or devices enables optical storage and computing, surpassing their electrical counterparts. In this paper, we propose a design of on-chip photonic convolution for optical in-memory computing by integrating the phase change chalcogenide of Ge2Sb2Se4Te1 (GSST) into an asymmetric directional coupler for constructions of an in-memory computing cell, marrying the advantages of both the large bandwidth of Mach-Zehnder interferometers (MZIs) and the small size of micro-ring resonators (MRRs). Through quasi-continuous electro-thermal tuning of the GSST-integrated in-memory computing cells, numerical calculations about the optical and electro-thermal behaviors during GSST phase transition confirm the tunability of the programmable elements stored in the in-memory computing cells within [-1, 1]. For proof-of-concept verification, we apply the proposed optical convolutional kernel to a typical image edge detection application. As evidenced by the evaluation results, the prototype achieves the same accuracy as the convolution kernel implemented on a common digital computer, demonstrating the feasibility of the proposed scheme for on-chip photonic convolution and optical in-memory computing.

Speeding up the classical simulation of Gaussian boson sampling with limited connectivity

Gaussian boson sampling (GBS) plays a crucially important role in demonstrating quantum advantage. As a major imperfection, the limited connectivity of the linear optical network weakens the quantum advantage result in recent experiments. In this work, we introduce an enhanced classical algorithm for simulating GBS processes with limited connectivity. It computes the loop Hafnian of an n × n symmetric matrix with bandwidth w in O ( n w 2 w ) time. It is better than the previous fastest algorithm which runs in O ( n w 2 2 w ) time. This classical algorithm is helpful on clarifying how limited connectivity affects the computational complexity of GBS and tightening the boundary for achieving quantum advantage in the GBS problem.

SiN integrated photonic components in the visible to near-infrared spectral region

Integrated photonics has emerged as one of the most promising platforms for quantum applications. The performances of quantum photonic integrated circuits (QPIC) necessitate a demanding optimization to achieve enhanced properties and tailored characteristics with more stringent requirements with respect to their classical counterparts. In this study, we report on the simulation, fabrication, and characterization of a series of fundamental components for photons manipulation in QPIC based on silicon nitride. These include crossing waveguides, multimode-interferometer-based integrated beam splitters (MMIs), asymmetric integrated Mach-Zehnder interferometers (MZIs) based on MMIs, and micro-ring resonators. Our investigation revolves primarily around the visible to near-infrared spectral region, as these integrated structures are meticulously designed and tailored for optimal operation within this wavelength range. By advancing the development of these elementary building blocks, we aim to pave the way for significant improvements in QPIC in a spectral region only little explored so far.

Programmable Photonic Time Circuits for Highly Scalable Universal Unitaries

Programmable photonic circuits (PPCs) have garnered substantial interest for their potential in facilitating deep learning accelerations and universal quantum computations. Although photonic computation using PPCs offers ultrafast operation, energy-efficient matrix calculations, and room-temperature quantum states, its poor scalability hinders integration. This challenge arises from the temporally one-shot operation of propagating light in conventional PPCs, resulting in a light-speed increase in device footprints. Here we propose the concept of programmable photonic time circuits, utilizing time-cycle-based computations analogous to gate cycling in the von Neumann architecture and quantum computation. Our building block is a reconfigurable SU(2) time gate, consisting of two resonators with tunable resonances, and coupled via time-coded dual-channel gauge fields. We demonstrate universal U(N) operations with high fidelity using an assembly of the SU(2) time gates, substantially improving scalability from O(N^{2}) to O(N) in terms of both the footprint and the number of gates. This result paves the way for PPC implementation in very large-scale integration.

Deep photonic network platform enabling arbitrary and broadband optical functionality

Expanding applications in optical communications, computing, and sensing continue to drive the need for high-performance integrated photonic components. Designing these on-chip systems with arbitrary functionality requires beyond what is possible with physical intuition, for which machine learning-based methods have recently become popular. However, computational demands for physically accurate device simulations present critical challenges, significantly limiting scalability and design flexibility of these methods. Here, we present a highly-scalable, physics-informed design platform for on-chip optical systems with arbitrary functionality, based on deep photonic networks of custom-designed Mach-Zehnder interferometers. Leveraging this platform, we demonstrate ultra-broadband power splitters and a spectral duplexer, each designed within two minutes. The devices exhibit state-of-the-art experimental performance with insertion losses below 0.66 dB, and 1-dB bandwidths exceeding 120 nm. This platform provides a tractable path towards systematic, large-scale photonic system design, enabling custom power, phase, and dispersion profiles for high-throughput communications, quantum information processing, and medical/biological sensing applications.

High-efficiency reinforcement learning with hybrid architecture photonic integrated circuit

Reinforcement learning (RL) stands as one of the three fundamental paradigms within machine learning and has made a substantial leap to build general-purpose learning systems. However, using traditional electrical computers to simulate agent-environment interactions in RL models consumes tremendous computing resources, posing a significant challenge to the efficiency of RL. Here, we propose a universal framework that utilizes a photonic integrated circuit (PIC) to simulate the interactions in RL for improving the algorithm efficiency. High parallelism and precision on-chip optical interaction calculations are implemented with the assistance of link calibration in the hybrid architecture PIC. By introducing similarity information into the reward function of the RL model, PIC-RL successfully accomplishes perovskite materials synthesis task within a 3472-dimensional state space, resulting in a notable 56% improvement in efficiency. Our results validate the effectiveness of simulating RL algorithm interactions on the PIC platform, highlighting its potential to boost computing power in large-scale and sophisticated RL tasks.

Iterative eigensolver using fixed-point photonic primitive

Photonic computing has potential advantages in speed and energy consumption yet is subject to inaccuracy due to the limited equivalent bitwidth of the analog signal. In this Letter, we demonstrate a configurable, fixed-point coherent photonic iterative solver for numerical eigenvalue problems using shifted inverse iteration. The photonic primitive can accommodate arbitrarily sized sparse matrix-vector multiplication and is deployed to solve eigenmodes in a photonic waveguide structure. The photonic iterative eigensolver does not accumulate errors from each iteration, providing a path toward implementing scientific computing applications on photonic primitives.

Quantitative comparison of the computational complexity of optical, digital and hybrid neural network architectures for image classification tasks

By implementing neuromorphic paradigms in processing visual information, machine learning became crucial in an ever-increasing number of applications of our everyday lives, ever more performing but also computationally demanding. While a pre-processing of the information passively in the optical domain, before optical-electronic conversion, can reduce the computational requirements for a machine learning task, a comprehensive analysis of computational requirements for hybrid optical-digital neural networks is thus far missing. In this work we critically compare and analyze the performance of different optical, digital and hybrid neural network architectures with respect to their classification accuracy and computational requirements for analog classification tasks of different complexity. We show that certain hybrid architectures exhibit a reduction of computational requirements of a factor >10 while maintaining their performance. This may inspire a new generation of co-designed optical-digital neural network architectures, aimed for applications that require low power consumption like remote sensing devices.

Neuromorphic Photonics Circuits: Contemporary Review

Neuromorphic photonics is a cutting-edge fusion of neuroscience-inspired computing and photonics technology to overcome the constraints of conventional computing architectures. Its significance lies in the potential to transform information processing by mimicking the parallelism and efficiency of the human brain. Using optics and photonics principles, neuromorphic devices can execute intricate computations swiftly and with impressive energy efficiency. This innovation holds promise for advancing artificial intelligence and machine learning while addressing the limitations of traditional silicon-based computing. Neuromorphic photonics could herald a new era of computing that is more potent and draws inspiration from cognitive processes, leading to advancements in robotics, pattern recognition, and advanced data processing. This paper reviews the recent developments in neuromorphic photonic integrated circuits, applications, and current challenges.

Reconfigurable Neuromorphic Computing: Materials, Devices, and Integration

Neuromorphic computing has been attracting ever-increasing attention due to superior energy efficiency, with great promise to promote the next wave of artificial general intelligence in the post-Moore era. Current approaches are, however, broadly designed for stationary and unitary assignments, thus encountering reluctant interconnections, power consumption, and data-intensive computing in that domain. Reconfigurable neuromorphic computing, an on-demand paradigm inspired by the inherent programmability of brain, can maximally reallocate finite resources to perform the proliferation of reproducibly brain-inspired functions, highlighting a disruptive framework for bridging the gap between different primitives. Although relevant research has flourished in diverse materials and devices with novel mechanisms and architectures, a precise overview remains blank and urgently desirable. Herein, the recent strides along this pursuit are systematically reviewed from material, device, and integration perspectives. At the material and device level, one comprehensively conclude the dominant mechanisms for reconfigurability, categorized into ion migration, carrier migration, phase transition, spintronics, and photonics. Integration-level developments for reconfigurable neuromorphic computing are also exhibited. Finally, a perspective on the future challenges for reconfigurable neuromorphic computing is discussed, definitely expanding its horizon for scientific communities.

Synchronous micromechanically resonant programmable photonic circuits

Programmable photonic integrated circuits (PICs) are emerging as powerful tools for control of light, with applications in quantum information processing, optical range finding, and artificial intelligence. Low-power implementations of these PICs involve micromechanical structures driven capacitively or piezoelectrically but are often limited in modulation bandwidth by mechanical resonances and high operating voltages. Here we introduce a synchronous, micromechanically resonant design architecture for programmable PICs and a proof-of-principle 1×8 photonic switch using piezoelectric optical phase shifters. Our design purposefully exploits high-frequency mechanical resonances and optically broadband components for larger modulation responses on the order of the mechanical quality factor Qm while maintaining fast switching speeds. We experimentally show switching cycles of all 8 channels spaced by approximately 11 ns and operating at 4.6 dB average modulation enhancement. Future advances in micromechanical devices with high Qm, which can exceed 10000, should enable an improved series of low-voltage and high-speed programmable PICs.

Efficient training of unitary optical neural networks

Deep learning has profoundly reshaped the technology landscape in numerous scientific areas and industrial sectors. This technology advancement is, nevertheless, confronted with severe bottlenecks in digital computing. Optical neural network presents a promising solution due to the ultra-high computing speed and energy efficiency. In this work, we present systematic study of unitary optical neural network (UONN) as an approach towards optical deep learning. Our results show that the UONN can be trained to high accuracy through special unitary gradient descent optimization, and the UONN is robust against physical imperfections and noises, hence it is more suitable for physical implementation than existing ONNs.

Auto-calibrating universal programmable photonic circuits: hardware error-correction and defect resilience

It is recently shown that discrete N × N linear unitary operators can be represented by interlacing N + 1 phase shift layers with a fixed intervening operator such as discrete fractional Fourier transform (DFrFT). Here, we show that introducing perturbations to the intervening operations does not compromise the universality of this architecture. Furthermore, we show that this architecture is resilient to defects in the phase shifters as long as no more than one faulty phase shifter is present in each layer. These properties enable post-fabrication auto-calibration of such universal photonic circuits, effectively compensating for fabrication errors and defects in phase components.

Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure

A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than a unitary coupled cluster with single and double excitations (qUCCSD), with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. As in the case of qUCCSD, exactly computing the energy scales factorially with system size on classical computers but polynomially on quantum devices. The local unitary cluster Jastrow ansatz removes the need for SWAP gates, can be tailored to arbitrary qubit topologies (e.g., square, hex, and heavy-hex), and is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers. The proposed family of ansatzes demonstrates that hardware efficiency and physical transparency are not mutually exclusive; indeed, chemical and physical intuition regarding electron correlation can illuminate a useful path towards hardware-friendly quantum circuits.

Generalized Quantum Measurements on a Higher-Dimensional System via Quantum Walks

Quantum measurements play a fundamental role in quantum mechanics. Especially, generalized quantum measurements provide a powerful and versatile tool to extract information from quantum systems. However, how to realize them on an arbitrary higher-dimensional quantum system remains a challenging task. Here we propose a simple recipe for the implementation of a general positive-operator valued measurement (POVM) on a higher-dimensional quantum system via a one-dimensional discrete-time quantum walk with a two-dimensional coin. Furthermore, using single photons and linear optics, we realize experimentally a symmetric, informationally complete (SIC) POVM on a three-dimensional system with high fidelity. As an application, we realize a qutrit state tomography with SIC-POVM and confirm that the infidelity scaling achieved by the qutrit SIC-POVM is as good as that based on mutually unbiased bases. Our study paves the way to explore physics and information in higher-dimensional quantum systems and finds applications in various quantum information processing tasks that rely on generalized quantum measurements.

Experimental simulation of symmetry-protected higher-order exceptional points with single photons

Exceptional points (EPs) of non-Hermitian (NH) systems have recently attracted increasing attention due to their rich phenomenology and intriguing applications. Compared to the predominantly studied second-order EPs, higher-order EPs have been assumed to play a much less prominent role because they generically require the tuning of more parameters. Here, we experimentally simulate two-dimensional topological NH band structures using single-photon interferometry, and observe topologically stable third-order EPs obtained by tuning only two real parameters in the presence of symmetry. In particular, we explore how different symmetries stabilize qualitatively different third-order EPs: the parity-time symmetry leads to a generic cube-root dispersion, while a generalized chiral symmetry implies a square-root dispersion coexisting with a flat band. Additionally, we simulate fourfold degeneracies, composed of the non-defective twofold degeneracies and second-order EPs. Our work reveals the abundant and conceptually richer higher-order EPs protected by symmetries and offers a versatile platform for further research on topological NH systems.

Time-Domain Universal Linear-Optical Operations for Universal Quantum Information Processing

We demonstrate universal and programmable three-mode linear-optical operations in the time domain by realizing a scalable dual-loop optical circuit suitable for universal quantum information processing (QIP). The programmability, validity, and deterministic operation of our circuit are demonstrated by performing nine different three-mode operations on squeezed-state pulses, fully characterizing the outputs with variable measurements, and confirming their entanglement. Our circuit can be scaled up just by making the outer loop longer and also extended to universal quantum computers by incorporating feed forward systems. Thus, our work paves the way to large-scale universal optical QIP.

Addressing the programming challenges of practical interferometric mesh based optical processors

We demonstrate a novel mesh of Mach-Zehnder interferometers (MZIs) for programmable optical processors. We thoroughly analyze the benefits and drawbacks of previously known meshes and compare our newly proposed mesh with these prior architectures, highlighting its unique features and advantages. The proposed mesh, referred to as Bokun mesh, is an architecture that merges the attributes of the prior topologies Diamond and Clements. Similar to Diamond, Bokun provides diagonal paths passing through every individual MZI enabling direct phase monitoring. However, unlike Diamond and similar to Clements, Bokun maintains a minimum optical depth leading to better scalability. Providing the monitoring option, Bokun's programming is faster improving the total energy efficiency of the processor. The performance of Bokun mesh enabled by an optimal optical depth is also more resilient to the loss and fabrication imperfections compared to architectures with longer depth such as Reck and Diamond. Employing an efficient programming scheme, the proposed architecture improves energy efficiency by 83% maintaining the same computation accuracy for weight matrix changes at 2 kHz.

Experimental quantum natural gradient optimization in photonics

Variational quantum algorithms (VQAs) combining the advantages of parameterized quantum circuits and classical optimizers, promise practical quantum applications in the noisy intermediate-scale quantum era. The performance of VQAs heavily depends on the optimization method. Compared with gradient-free and ordinary gradient descent methods, the quantum natural gradient (QNG), which mirrors the geometric structure of the parameter space, can achieve faster convergence and avoid local minima more easily, thereby reducing the cost of circuit executions. We utilized a fully programmable photonic chip to experimentally estimate the QNG in photonics for the first time, to the best of our knowledge. We obtained the dissociation curve of the He-H⁺ cation and achieved chemical accuracy, verifying the outperformance of QNG optimization on a photonic device. Our work opens up a vista of utilizing QNG in photonics to implement practical near-term quantum applications.

Multichip multidimensional quantum networks with entanglement retrievability

Quantum networks provide the framework for quantum communication, clock synchronization, distributed quantum computing, and sensing. Implementing large-scale and practical quantum networks relies on the development of scalable architecture and integrated hardware that can coherently interconnect many remote quantum nodes by sharing multidimensional entanglement through complex-medium quantum channels. We demonstrate a multichip multidimensional quantum entanglement network based on mass-manufacturable integrated-nanophotonic quantum node chips fabricated on a silicon wafer by means of complementary metal-oxide-semiconductor processes. Using hybrid multiplexing, we show that multiple multidimensional entangled states can be distributed across multiple chips connected by few-mode fibers. We developed a technique that can efficiently retrieve multidimensional entanglement in complex-medium quantum channels, which is important for practical uses. Our work demonstrates the enabling capabilities of realizing large-scale practical chip-based quantum entanglement networks.

Transferable learning on analog hardware

While analog neural network (NN) accelerators promise massive energy and time savings, an important challenge is to make them robust to static fabrication error. Present-day training methods for programmable photonic interferometer circuits, a leading analog NN platform, do not produce networks that perform well in the presence of static hardware errors. Moreover, existing hardware error correction techniques either require individual retraining of every analog NN (which is impractical in an edge setting with millions of devices), place stringent demands on component quality, or introduce hardware overhead. We solve all three problems by introducing one-time error-aware training techniques that produce robust NNs that match the performance of ideal hardware and can be exactly transferred to arbitrary highly faulty photonic NNs with hardware errors up to five times larger than present-day fabrication tolerances.

Demonstration of Hong-Ou-Mandel interference in an LNOI directional coupler

Interference between single photons is key for many quantum optics experiments and applications in quantum technologies, such as quantum communication or computation. It is advantageous to operate the systems at telecommunication wavelengths and to integrate the setups for these applications in order to improve stability, compactness and scalability. A new promising material platform for integrated quantum optics is lithium niobate on insulator (LNOI). Here, we realise Hong-Ou-Mandel (HOM) interference between telecom photons from an engineered parametric down-conversion source in an LNOI directional coupler. The coupler has been designed and fabricated in house and provides close to perfect balanced beam splitting. We obtain a raw HOM visibility of (93.5 ± 0.7) %, limited mainly by the source performance and in good agreement with off-chip measurements. This lays the foundation for more sophisticated quantum experiments in LNOI.

Ultrafast Temporal SU(1,1) Interferometer

Interferometers are highly sensitive to phase differences and are utilized in numerous schemes. Of special interest is the quantum SU(1,1) interferometer which is able to improve the sensitivity of classical interferometers. We theoretically develop and experimentally demonstrate a temporal SU(1,1) interferometer based on two time lenses in a 4f configuration. This temporal SU(1,1) interferometer has a high temporal resolution, imposes interference on both time and spectral domains, and is sensitive to the phase derivative which is important for detecting ultrafast phase changes. Therefore, this interferometer can be utilized for temporal mode encoding, imaging, and studying the ultrafast temporal structure of quantum light.

Photonic Hopfield neural network for the Ising problem

The Ising problem, a vital combinatorial optimization problem in various fields, is hard to solve by traditional Von Neumann computing architecture on a large scale. Thus, lots of application-specific physical architectures are reported, including quantum-based, electronics-based, and optical-based platforms. A Hopfield neural network combined with a simulated annealing algorithm is considered one of the effective approaches but is still limited by large resource consumption. Here, we propose to accelerate the Hopfield network on a photonic integrated circuit composed of the arrays of Mach-Zehnder interferometer. Our proposed Photonic Hopfield Neural Network (PHNN), utilizing the massively parallel operations and integrated circuit with ultrafast iteration rate, converges to a stable ground state solution with high probability. The average success probabilities for the MaxCut problem with a problem size of 100 and the Spin-glass problem with a problem size of 60 can both reach more than 80%. Moreover, our proposed architecture is inherently robust to the noise induced by the imperfect characteristics of components on chip.

Parallel photonic acceleration processor for matrix-matrix multiplication

We propose and experimentally demonstrate a highly parallel photonic acceleration processor based on a wavelength division multiplexing (WDM) system and a non-coherent Mach-Zehnder interferometer (MZI) array for matrix-matrix multiplication. The dimensional expansion is achieved by WDM devices, which play a crucial role in realizing matrix-matrix multiplication together with the broadband characteristics of an MZI. We implemented a 2 × 2 arbitrary nonnegative valued matrix using a reconfigurable 8 × 8 MZI array structure. Through experimentation, we verified that this structure could achieve 90.5% inference accuracy in a classification task for the Modified National Institute of Standards and Technology (MNIST) handwritten dataset. This provides a new effective solution for large-scale integrated optical computing systems based on convolution acceleration processors.

Microring-based programmable coherent optical neural networks

Coherent programmable integrated photonics circuits have shown great potential as specialized hardware accelerators for deep learning tasks, which usually involve the use of linear matrix multiplication and nonlinear activation components. We design, simulate and train an optical neural network fully based on microring resonators, which shows advantages in terms of device footprint and energy efficiency. We use tunable coupled double ring structures as the interferometer components for the linear multiplication layers and modulated microring resonators as the reconfigurable nonlinear activation components. We then develop optimization algorithms to train the direct tuning parameters such as applied voltages based on the transfer matrix method and using automatic differentiation for all optical components.

Artificial Intelligence and Advanced Materials

Artificial intelligence (AI) is gaining strength, and materials science can both contribute to and profit from it. In a simultaneous progress race, new materials, systems, and processes can be devised and optimized thanks to machine learning (ML) techniques, and such progress can be turned into innovative computing platforms. Future materials scientists will profit from understanding how ML can boost the conception of advanced materials. This review covers aspects of computation from the fundamentals to directions taken and repercussions produced by computation to account for the origins, procedures, and applications of AI. ML and its methods are reviewed to provide basic knowledge of its implementation and its potential. The materials and systems used to implement AI with electric charges are finding serious competition from other information-carrying and processing agents. The impact these techniques have on the inception of new advanced materials is so deep that a new paradigm is developing where implicit knowledge is being mined to conceive materials and systems for functions instead of finding applications to found materials. How far this trend can be carried is hard to fathom, as exemplified by the power to discover unheard of materials or physical laws buried in data.

Fast reconstruction of programmable integrated interferometers

Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing optical interferometers that could implement arbitrary transformations of input fields even in the case of high manufacturing errors. The building of detailed models of such devices drastically increases the efficiency of their practical use. The integral design of interferometers complicates its reconstruction since the internal elements are hard to address. This problem can be approached by using optimization algorithms [Opt. Express29, 38429 (2021)10.1364/OE.432481]. In this paper, we present what we believe to be a novel efficient algorithm based on linear algebra only, which does not use computationally expensive optimization procedures. We show that this approach makes it possible to perform fast and accurate characterization of high-dimensional programmable integrated interferometers. Moreover, the method provides access to the physical characteristics of individual interferometer layers.

Experimentally realized in situ backpropagation for deep learning in photonic neural networks

Integrated photonic neural networks provide a promising platform for energy-efficient, high-throughput machine learning with extensive scientific and commercial applications. Photonic neural networks efficiently transform optically encoded inputs using Mach-Zehnder interferometer mesh networks interleaved with nonlinearities. We experimentally trained a three-layer, four-port silicon photonic neural network with programmable phase shifters and optical power monitoring to solve classification tasks using "in situ backpropagation," a photonic analog of the most popular method to train conventional neural networks. We measured backpropagated gradients for phase-shifter voltages by interfering forward- and backward-propagating light and simulated in situ backpropagation for 64-port photonic neural networks trained on MNIST image recognition given errors. All experiments performed comparably to digital simulations ([Formula: see text]94% test accuracy), and energy scaling analysis indicated a route to scalable machine learning.

Hardware Error Correction for MZI-Based Matrix Computation

With the rapid development of artificial intelligence, the electronic system has fallen short of providing the needed computation speed. It is believed that silicon-based optoelectronic computation may be a solution, where Mach-Zehnder interferometer (MZI)-based matrix computation is the key due to its advantages of simple implementation and easy integration on a silicon wafer, but one of the concerns is the precision of the MZI method in the actual computation. This paper will identify the main hardware error sources of MZI-based matrix computation, summarize the available hardware error correction methods from the perspective of the entire MZI meshes and a single MZI device, and propose a new architecture that will largely improve the precision of MZI-based matrix computation without increasing the size of the MZI's mesh, which may lead to a fast and accurate optoelectronic computing system.

Large Baseline Optical Imaging Assisted by Single Photons and Linear Quantum Optics

In this Letter, we show that by combining quantum metrology and networking tools, it is possible to extend the baseline of an interferometric optical telescope and thus improve diffraction-limited imaging of point source positions. The quantum interferometer is based on single-photon sources, linear optical circuits, and efficient photon number counters. Surprisingly, with thermal (stellar) sources of low photon number per mode and high transmission losses across the baseline, the detected photon probability distribution still retains a large amount of Fisher information about the source position, allowing for a significant improvement in the resolution of positioning point sources, on the order of 10  μas. Our proposal can be implemented with current technology. In particular, our proposal does not require experimental optical quantum memories.

Heavy tails and pruning in programmable photonic circuits for universal unitaries

Developing hardware for high-dimensional unitary operators plays a vital role in implementing quantum computations and deep learning accelerations. Programmable photonic circuits are singularly promising candidates for universal unitaries owing to intrinsic unitarity, ultrafast tunability and energy efficiency of photonic platforms. Nonetheless, when the scale of a photonic circuit increases, the effects of noise on the fidelity of quantum operators and deep learning weight matrices become more severe. Here we demonstrate a nontrivial stochastic nature of large-scale programmable photonic circuits-heavy-tailed distributions of rotation operators-that enables the development of high-fidelity universal unitaries through designed pruning of superfluous rotations. The power law and the Pareto principle for the conventional architecture of programmable photonic circuits are revealed with the presence of hub phase shifters, allowing for the application of network pruning to the design of photonic hardware. For the Clements design of programmable photonic circuits, we extract a universal architecture for pruning random unitary matrices and prove that "the bad is sometimes better to be removed" to achieve high fidelity and energy efficiency. This result lowers the hurdle for high fidelity in large-scale quantum computing and photonic deep learning accelerators.

Efficient quantum analytic nuclear gradients with double factorization

Efficient representations of the Hamiltonian, such as double factorization, drastically reduce the circuit depth or the number of repetitions in error corrected and noisy intermediate-scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically simulated examples with up to 327 quantum and 18 470 total atoms in QM/MM simulations with modest-sized quantum active spaces. We show this in the context of the variational quantum eigensolver in case studies, such as transition state optimization, ab initio molecular dynamics simulation, and energy minimization of large molecular systems.