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.

Single-shot optical neural network.

Analog optical and electronic hardware has emerged as a promising alternative to digital electronics to improve the efficiency of deep neural networks (DNNs). However, previous work has been limited in scalability (input vector length K ≈ 100 elements) or has required nonstandard DNN models and retraining, hindering widespread adoption. Here, we present an analog, CMOS-compatible DNN processor that uses free-space optics to reconfigurably distribute an input vector and optoelectronics for static, updatable weighting and the nonlinearity-with K ≈ 1000 and beyond. We demonstrate single-shot-per-layer classification of the MNIST, Fashion-MNIST, and QuickDraw datasets with standard fully connected DNNs, achieving respective accuracies of 95.6, 83.3, and 79.0% without preprocessing or retraining. We also experimentally determine the fundamental upper bound on throughput (∼0.9 exaMAC/s), set by the maximum optical bandwidth before substantial increase in error. Our combination of wide spectral and spatial bandwidths enables highly efficient computing for next-generation DNNs.

Asymptotically fault-tolerant programmable photonics.

Component errors limit the scaling of programmable coherent photonic circuits. These errors arise because the standard tunable photonic coupler-the Mach-Zehnder interferometer (MZI)-cannot be perfectly programmed to the cross state. Here, we introduce two modified circuit architectures that overcome this limitation: (1) a 3-splitter MZI mesh for generic errors, and (2) a broadband MZI+Crossing design for correlated errors. Because these designs allow for perfect realization of the cross state, the matrix fidelity no longer degrades with increased mesh size, allowing scaling to arbitrarily large meshes. The proposed architectures support progressive self-configuration, are more compact than previous MZI-doubling schemes, and do not require additional phase shifters. This removes a key limitation to the development of very-large-scale programmable photonic circuits.

Delocalized photonic deep learning on the internet's edge.

Advanced machine learning models are currently impossible to run on edge devices such as smart sensors and unmanned aerial vehicles owing to constraints on power, processing, and memory. We introduce an approach to machine learning inference based on delocalized analog processing across networks. In this approach, named Netcast, cloud-based "smart transceivers" stream weight data to edge devices, enabling ultraefficient photonic inference. We demonstrate image recognition at ultralow optical energy of 40 attojoules per multiply (<1 photon per multiply) at 98.8% (93%) classification accuracy. We reproduce this performance in a Boston-area field trial over 86 kilometers of deployed optical fiber, wavelength multiplexed over 3 terahertz of optical bandwidth. Netcast allows milliwatt-class edge devices with minimal memory and processing to compute at teraFLOPS rates reserved for high-power (>100 watts) cloud computers.

Freely scalable and reconfigurable optical hardware for deep learning.

As deep neural network (DNN) models grow ever-larger, they can achieve higher accuracy and solve more complex problems. This trend has been enabled by an increase in available compute power; however, efforts to continue to scale electronic processors are impeded by the costs of communication, thermal management, power delivery and clocking. To improve scalability, we propose a digital optical neural network (DONN) with intralayer optical interconnects and reconfigurable input values. The path-length-independence of optical energy consumption enables information locality between a transmitter and a large number of arbitrarily arranged receivers, which allows greater flexibility in architecture design to circumvent scaling limitations. In a proof-of-concept experiment, we demonstrate optical multicast in the classification of 500 MNIST images with a 3-layer, fully-connected network. We also analyze the energy consumption of the DONN and find that digital optical data transfer is beneficial over electronics when the spacing of computational units is on the order of [Formula: see text]m.

Design of high-speed phase-only spatial light modulators with two-dimensional tunable microcavity arrays.

Spatial light modulators (SLMs) are central to numerous applications ranging from high-speed displays to adaptive optics, structured illumination microscopy, and holography. After decades of advances, SLM arrays based on liquid crystals can now reach large pixel counts exceeding 106 with phase-only modulation with a pixel pitch of less than 10 µm and reflectance around 75%. However, the rather slow modulation speed in such SLMs (below hundreds of Hz) presents limitations for many applications. Here we propose an SLM architecture that can achieve two-dimensional phase-only modulation at high speed in excess of GHz. The architecture consists of a tunable two-dimensional array of vertically oriented, one-sided microcavities that are tuned through an electro-optic material such as barium titanate (BTO). We calculate that the optimized microcavity design achieves a π phase shift under an applied bias voltage below 10 V, while maintaining nearly constant reflection amplitude. As two model applications, we consider high-speed 2D beam steering as well as beam forming. The outlined design methodology could also benefit future design of spatial light modulators with other specifications (for example amplitude modulators). This high-speed SLM architecture promises a wide range of new applications ranging from fully tunable metasurfaces to optical computing accelerators, high-speed interconnects, true 2D phased array beam steering, and quantum computing with cold atom arrays.

Experimental investigation of performance differences between coherent Ising machines and a quantum annealer.

Physical annealing systems provide heuristic approaches to solving combinatorial optimization problems. Here, we benchmark two types of annealing machines-a quantum annealer built by D-Wave Systems and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillators-on two problem classes, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on cubic graphs. On denser problems, however, we observe an exponential penalty for the quantum annealer [exp(-αDW N 2)] relative to CIMs [exp(-αCIM N)] for fixed anneal times, both on the SK model and on 50% edge density MAX-CUT. This leads to a several orders of magnitude time-to-solution difference for instances with over 50 vertices. An optimal-annealing time analysis is also consistent with a substantial projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the fully-connected CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.

Temporal Simultons in Optical Parametric Oscillators.

We report the first demonstration of a regime of operation in optical parametric oscillators (OPOs), in which the formation of temporal simultons produces stable femtosecond half-harmonic pulses. Simultons are simultaneous bright-dark solitons of a signal field at frequency ω and the pump field at 2ω, which form in a quadratic nonlinear medium. The formation of simultons in an OPO is due to the interplay of nonlinear pulse acceleration with the timing mismatch between the pump repetition period and the cold-cavity round-trip time and is evidenced by sech^{2} spectra with broad instantaneous bandwidths when the resonator is detuned to a slightly longer round-trip time than the pump repetition period. We provide a theoretical description of an OPO operating in a regime dominated by these dynamics, observe the distinct features of simulton formation in an experiment, and verify our results with numerical simulations. These results represent a new regime of operation in nonlinear resonators, which can lead to efficient and scalable sources of few-cycle frequency combs at arbitrary wavelengths.

A fully programmable 100-spin coherent Ising machine with all-to-all connections.

Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.

A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems.

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.

Advantages of coherent feedback for cooling quantum oscillators.

We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process noncommuting output field quadratures simultaneously without loss of fidelity, and may provide important clues for the design of coherent feedback schemes for more general problems of nonlinear and robust control.