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AI and Optical Data Sciences

Spatial Ising machine: photonic acceleration and adiabatic evolution

Claudio Conti

Published Mar 9, 2021• 0 citations
Publisher

Abstract

Spatial Ising Machines are simple optical acceleration devices enabling hard combinatorial optimization with millions of spins. We review our results, including noise acceleration and adiabatic evolution.
DOI
10.1117/12.2585739

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We show how spatial light modulation allows one to optically compute an Ising Hamiltonian. This enables the use of optical radiation to accelerate algorithms to find the ground state and hence the optimal solution of a combinatorial optimization problem. The phase matrix on a spatial light modulator acts as a lattice of spins whose interaction is ruled by the constrained optical intensity in the far field. Feedback from the detection plane allows the spatial phase distribution to evolve toward the minimum of the selected spin model. Related topics such as annealing, adiabatic evolution, the XY model, and decomposition methods are reviewed.
Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware. Novel optical platforms, known as coherent or photonic Ising machines, are attracting considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-known technique based on adiabatic evolution for finding optimal solutions in classical and quantum systems made by atoms, electrons, or photons. Although various Ising machines employ annealing in some form, adiabatic computing on optical settings has been only partially investigated. Here, we realize the adiabatic evolution of frustrated Ising models with 100 spins programmed by spatial light modulation. We use holographic and optical control to change the spin couplings adiabatically, and exploit experimental noise to explore the energy landscape. Annealing enhances the convergence to the Ising ground state and allows to find the problem solution with probability close to unity. Our results demonstrate a photonic scheme for combinatorial optimization in analogy with adiabatic quantum algorithms and classical annealing methods but enforced by optical vector-matrix multiplications and scalable photonic technology.
A spatial photonic Ising machine (SPIM) handles large-scale combinatorial optimization problems due to optical processing with spatial parallelism. However, iterative feedback in the search for an optimal solution limits processing speed, even though the Ising Hamiltonian is computed optically. We propose a parallel spatial photonic Ising machine (pSPIM) utilizing spatial multiplexing to search for an optimal solution efficiently. By employing grating patterns and encoding multiple configurations of Ising spins in a phase distribution, several Ising Hamiltonians are computed simultaneously. We demonstrated that the optimal solutions of max-cut problems with 100 Ising spins were obtained more frequently as the number of processing units increased. In addition, combining the multicomponent model with parallel processing provides an efficient search for optimal solutions to problems represented by using interaction matrices with a rank greater than one. The spin-update strategy of pSPIM offers an effective approach for efficiently solving large-scale combinatorial optimization problems.
Abstract Ising machines are novel computing devices for the energy minimization of Ising models. These combinatorial optimization problems are of paramount importance for science and technology, but remain difficult to tackle on large scale by conventional electronics. Recently, various photonics‐based Ising machines demonstrated fast computing of a Ising ground state by data processing through multiple temporal or spatial optical channels. Experimental noise acts as a detrimental effect in many of these devices. On the contrary, here we demonstrate that an optimal noise level enhances the performance of spatial‐photonic Ising machines on frustrated spin problems. By controlling the error rate at the detection, we introduce a noisy‐feedback mechanism in an Ising machine based on spatial light modulation. We investigate the device performance on systems with hundreds of individually‐addressable spins with all‐to‐all couplings and we found an increased success probability at a specific noise level. The optimal noise amplitude depends on graph properties and size, thus indicating an additional tunable parameter helpful in exploring complex energy landscapes and in avoiding getting stuck in local minima. Our experimental results identify noise as a potentially valuable resource for optical computing. This concept, which also holds in different nanophotonic neural networks, may be crucial in developing novel hardware with optics‐enabled parallel architecture for large‐scale optimizations.
Abstract 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 optimization problems. As a computing accelerator, large-scale photonic spatial Ising machine have great advantages and potentials due to excellent scalability and compact system. However, current fundamental limitation of photonic spatial Ising machine is the configuration flexibility of problem implementation in the accelerator model. Arbitrary spin interaction is highly desired for solving various NP hard problems. Moreover, the absence of external magnetic field in the proposed photonic Ising machine will further narrow the freedom to map the optimization applications. In this paper, we propose a novel quadrature photonic spatial Ising machine to break through the limitation of photonic Ising accelerator by synchronous phase manipulation in two and three sections. Max-cut problem solution with graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100 iterations. We derive and verify using simulation the solution for Max-cut problem with more than 1600 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 achieve the optimal solution. Our work suggests flexible problem solution by large-scale photonic spatial Ising machine.