Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines

TL;DR

This paper presents a new method for encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines, enabling broader application to complex optimization problems with improved control and scalability.

Contribution

We introduce a direct control technique for the interaction matrix in SPIMs, allowing encoding of arbitrary couplings and connectivity, validated through experiments and problem solving.

Findings

Experimental validation of the new encoding method.

Successful solution of graph partitioning problems.

Enhanced applicability of SPIMs to real-world NP problems.

Abstract

Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising Machines have proven to be advantageous for simulating fully connected large-scale spin systems. However, fine control of a general interaction matrix $J$ has so far only been accomplished through eigenvalue decomposition methods that either limit the scalability or increase the execution time of the optimization process. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, enabling the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected values and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach greatly expands the applicability of SPIMs for real-world applications without sacrificing any of the inherent advantages of the system, and paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models, on SPIM devices.