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There has been a resurgence of interest in optical computing since the early 2010s, both in academia and in industry, with much of the excitement centred around special-purpose optical computers for neural-network processing. Optical computing has been a topic of periodic study since the 1960s, including for neural networks in the 1980s and early 1990s, and a wide variety of optical-computing schemes and architectures have been proposed. In this Perspective article, we provide a systematic explanation of why and how optics might be able to give speed or energy-efficiency benefits over electronics for computing, enumerating 11 features of optics that can be harnessed when designing an optical computer. One often-mentioned motivation for optical computing — that the speed of light is fast — is emphatically not a key differentiating physical property of optics for computing; understanding where an advantage could come from is more subtle. We discuss how gaining an advantage over state-of-the-art electronic processors will likely only be achievable by careful design that harnesses more than 1 of the 11 features, while avoiding a number of pitfalls that we describe.Optical computing has the potential to be faster and more energy-efficient than conventional digital-electronic computing for certain applications. This Perspective article surveys the differences between optics and electronics that could be exploited, and explores the physics and engineering challenges in realizing useful optical computers.

Ising machines are hardware solvers that aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because any problem in the complexity class NP can be formulated as an Ising problem with only polynomial overhead, and thus a scalable Ising machine that outperforms existing standard digital computers could have a huge impact for practical applications. We survey the status of various approaches to constructing Ising machines and explain their underlying operational principles. The types of Ising machines considered here include classical thermal annealers based on technologies such as spintronics, optics, memristors and digital hardware accelerators; dynamical systems solvers implemented with optics and electronics; and superconducting-circuit quantum annealers. We compare and contrast their performance using standard metrics such as the ground-state success probability and time-to-solution, give their scaling relations with problem size, and discuss their strengths and weaknesses.Minimizing the energy of the Ising model is a prototypical combinatorial optimization problem, ubiquitous in our increasingly automated world. This Review surveys Ising machines — special-purpose hardware solvers for this problem — and examines the various operating principles and compares their performance.

Nonlinearity is crucial for sophisticated tasks in machine learning but is often difficult to engineer outside of electronics. By encoding the inputs in parameters of the system, linear systems can realize efficiently trainable nonlinear computations.

Deep learning has become a widespread tool in both science and industry. However, continued progress is hampered by the rapid growth in energy costs of ever-larger deep neural networks. Optical neural networks provide a potential means to solve the energy-cost problem faced by deep learning. Here, we experimentally demonstrate an optical neural network based on optical dot products that achieves 99% accuracy on handwritten-digit classification using ~3.1 detected photons per weight multiplication and ~90% accuracy using ~0.66 photons (~2.5 × 10 −19  J of optical energy) per weight multiplication. The fundamental principle enabling our sub-photon-per-multiplication demonstration—noise reduction from the accumulation of scalar multiplications in dot-product sums—is applicable to many different optical-neural-network architectures. Our work shows that optical neural networks can achieve accurate results using extremely low optical energies. Though theory suggests that highly energy efficient optical neural networks (ONNs) based on optical matrix-vector multipliers are possible, an experimental validation is lacking. Here, the authors report an ONN with >90% accuracy image classification using <1 detected photon per scalar multiplication.

Photonic simulators using synthetic frequency dimensions have enabled flexible experimental analogues of condensed-matter systems. However, so far, such photonic simulators have been limited in scale, yielding results that suffer from finite-size effects. Here we present an analogue simulator capable of simulating large two-dimensional (2D) and 3D lattices, as well as lattices with non-planar connectivity. Our simulator takes advantage of the broad bandwidth achievable in photonics, allowing our experiment to realize programmable lattices with over 100,000 lattice sites. We showcase the scale of our simulator by demonstrating the extension of bandstructure spectroscopy from 1D to 2D and 3D lattices. We then report the direct observation of time-reversal symmetry-breaking in a triangular lattice in both momentum and real space, as well as site-resolved occupation measurements in a tree-like geometry that serves as a toy model in quantum gravity. Moreover, we demonstrate a method to excite arbitrary multisite states, which we use to study the response of a 2D lattice to both conventional and exotic input states. Our work highlights the scalability and flexibility of optical synthetic frequency dimensions. Future experiments building on our approach will be able to explore non-equilibrium phenomena in high-dimensional lattices and to simulate models with nonlocal higher-order interactions.Analogue photonic simulators have so far suffered from severe finite size effects and limited programmability. Now, a frequency-mode photonic simulator enables the simulation of large-scale models in two and three dimensions.

Deep-learning models have become pervasive tools in science and engineering. However, their energy requirements now increasingly limit their scalability 1 . Deep-learning accelerators 2 – 9 aim to perform deep learning energy-efficiently, usually targeting the inference phase and often by exploiting physical substrates beyond conventional electronics. Approaches so far 10 – 22 have been unable to apply the backpropagation algorithm to train unconventional novel hardware in situ. The advantages of backpropagation have made it the de facto training method for large-scale neural networks, so this deficiency constitutes a major impediment. Here we introduce a hybrid in situ–in silico algorithm, called physics-aware training, that applies backpropagation to train controllable physical systems. Just as deep learning realizes computations with deep neural networks made from layers of mathematical functions, our approach allows us to train deep physical neural networks made from layers of controllable physical systems, even when the physical layers lack any mathematical isomorphism to conventional artificial neural network layers. To demonstrate the universality of our approach, we train diverse physical neural networks based on optics, mechanics and electronics to experimentally perform audio and image classification tasks. Physics-aware training combines the scalability of backpropagation with the automatic mitigation of imperfections and noise achievable with in situ algorithms. Physical neural networks have the potential to perform machine learning faster and more energy-efficiently than conventional electronic processors and, more broadly, can endow physical systems with automatically designed physical functionalities, for example, for robotics 23 – 26 , materials 27 – 29 and smart sensors 30 – 32 . A hybrid algorithm that applies backpropagation is used to train layers of controllable physical systems to carry out calculations like deep neural networks, but accounting for real-world noise and imperfections.

Optical imaging is commonly used for both scientific and technological applications across industry and academia. In image sensing, a measurement, such as of an object’s position or contour, is performed by computational analysis of a digitized image. An emerging image-sensing paradigm relies on optical systems that—instead of performing imaging—act as encoders that optically compress images into low-dimensional spaces by extracting salient features; however, the performance of these encoders is typically limited by their linearity. Here we report a nonlinear, multilayer optical neural network (ONN) encoder for image sensing based on a commercial image intensifier as an optical-to-optical nonlinear activation function. This nonlinear ONN outperforms similarly sized linear optical encoders across several representative tasks, including machine-vision benchmarks, flow-cytometry image classification and identification of objects in a three-dimensionally printed real scene. For machine-vision tasks, especially those featuring incoherent broadband illumination, our concept allows for a considerable reduction in the requirement of camera resolution and electronic post-processing complexity. In general, image pre-processing with ONNs should enable image-sensing applications that operate accurately with fewer pixels, fewer photons, higher throughput and lower latency.A nonlinear optical neural network image sensor based on an image intensifier enables efficient all-optical image encoding for a variety of machine-vision tasks.

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

Energy efficiency in computation is ultimately limited by noise, with quantum limits setting the fundamental noise floor. Analog physical neural networks hold promise for improved energy efficiency compared to digital electronic neural networks. However, they are typically operated in a relatively high-power regime so that the signal-to-noise ratio (SNR) is large (>10), and the noise can be treated as a perturbation. We study optical neural networks where all layers except the last are operated in the limit that each neuron can be activated by just a single photon, and as a result the noise on neuron activations is no longer merely perturbative. We show that by using a physics-based probabilistic model of the neuron activations in training, it is possible to perform accurate machine-learning inference in spite of the extremely high shot noise (SNR  ~ 1). We experimentally demonstrated MNIST handwritten-digit classification with a test accuracy of 98% using an optical neural network with a hidden layer operating in the single-photon regime; the optical energy used to perform the classification corresponds to just 0.038 photons per multiply-accumulate (MAC) operation. Our physics-aware stochastic training approach might also prove useful with non-optical ultra-low-power hardware. Neural networks on analog physical devices often struggle with low computational precision. Here, authors developed an approach that enables neural networks to effectively exploit highly stochastic systems, achieving high performance even under an extremely low signal-to-noise ratio.

Quantum reservoir computing (QRC) has been proposed as a paradigm for performing machine learning with quantum processors where the training takes place in the classical domain, avoiding the issue of barren plateaus in parameterized-circuit quantum neural networks. It is natural to consider using a quantum processor based on microwave superconducting circuits to classify microwave signals that are analog—continuous in time. However, while there have been theoretical proposals of analog QRC, to date QRC has been implemented using the circuit model—imposing a discretization of the incoming signal in time. In this paper we show how a quantum superconducting circuit comprising an oscillator coupled to a qubit can be used as an analog quantum reservoir for a variety of classification tasks, achieving high accuracy on all of them. Our work demonstrates processing of ultra-low-power microwave signals within our superconducting circuit, a step towards achieving a quantum sensing-computational advantage on impinging microwave signals. Quantum reservoir computing might in principle give advantages in solving signal classification tasks, but current implementations usually incur in the digitalization bottleneck. Here, the authors demonstrate an implementation dealing directly with the analogue MW signals.