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The mining in physics and biology for accelerating the hardcore algorithm to solve non-deterministic polynomial (NP) hard problems has inspired a great amount of special-purpose ma-chine models. Ising machine has become an efficient solver for various combinatorial optimizationproblems. As a computing accelerator, large-scale photonic spatial Ising machine have great advan-tages and potentials due to excellent scalability and compact system. However, current fundamentallimitation of photonic spatial Ising machine is the configuration flexibility of problem implementationin the accelerator model. Arbitrary spin interactions is highly desired for solving various NP hardproblems. Moreover, the absence of external magnetic field in the proposed photonic Ising machinewill further narrow the freedom to map the optimization applications. In this paper, we propose anovel quadrature photonic spatial Ising machine to break through the limitation of photonic Isingaccelerator by synchronous phase manipulation in two and three sections. Max-cut problem solutionwith graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100iterations. We derive and verify using simulation the solution for Max-cut problem with more than1600 nodes and the system tolerance for light misalignment. Moreover, vertex cover problem, modeled as an Ising model with external magnetic field, has been successfully implemented to achievethe optimal solution. Our work suggests flexible problem solution by large-scale photonic spatialIsing machine.
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Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground state search of an antiferromagnetic model with $40000$ spins in number-partitioning problem. Thus such an optoelectronic computing exhibits great programmability and scalability for the practical applications of studying statistical systems and combinatorial optimization problems.
Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Thanks to gauge transformation, we experimentally evaluate the phase diagram of high-dimensional spin-glass equilibrium system with $100$ fully-connected spins. We observe the presence of paramagnetic, ferromagnetic as well as spin-glass phases and determine the critical temperature $T_c$ and the critical probability ${{p}_{c}}$ of phase transitions, which agree well with the mean-field theory predictions. Thus the approximation of the mean-field model is experimentally validated in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions, even when the system is associated with the optical aberrations and the measurement uncertainty.
We review some of the basic principles, fundamentals, technologies, architectures and recent advances leading to thefor the implementation of Field Programmable Photonic Field Arrays (FPPGAs).
Neural networks have enabled applications in artificial intelligence through machine learning, and neuromorphic computing. Software implementations of neural networks on conventional computers that have separate memory and processor (and that operate sequentially) are limited in speed and energy efficiency. Neuromorphic engineering aims to build processors in which hardware mimics neurons and synapses in the brain for distributed and parallel processing. Neuromorphic engineering enabled by photonics (optical physics) can offer sub-nanosecond latencies and high bandwidth with low energies to extend the domain of artificial intelligence and neuromorphic computing applications to machine learning acceleration, nonlinear programming, intelligent signal processing, etc. Photonic neural networks have been demonstrated on integrated platforms and free-space optics depending on the class of applications being targeted. Here, we discuss the prospects and demonstrated applications of these photonic neural networks.
In photonic neural network a key building block is the perceptron. Here, we describe and demonstrate a complex-valued photonic perceptron that combines time and space multiplexing in a fully passive silicon photonics integrated circuit. An input time dependent bit sequence is broadcasted into a few delay lines where the relative phases are trained by particle swarm algorithms toward the given task. Since only the phases of the propagating optical modes are trained, signal attenuation in the perceptron due to amplitude modulation is avoided. The perceptron performs binary pattern recognition and few bit delayed XOR operations up to 16 Gbps (limited by the used electronics) with Bit Error Rates as low as $10^{-6}$. The perceptron is fully integrated, silicon based, scalable, and can be used as a building block in large neural networks.
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