Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines

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 demon-
strate 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.