# Incorporating rank-free coupling and external field via an incoherent modulated spatial photonic Ising machine

arXiv: https://arxiv.org/abs/2512.21587 · HTML: https://mlsanity.com/paper/2512.21587/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 36 references that are in the map.
- First posted on arXiv 25 Dec 2025.

## Builds on (most cited first, 3 of 3)

- [Deep Graph Convolutional Reinforcement Learning for Financial Portfolio Management -- DeepPocket](https://mlsanity.com/paper/2105.08664/) (2021)
- [Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machine](https://mlsanity.com/paper/2303.14993/) (2023)
- [Temporal compressive edge imaging enabled by a lensless diffuser camera](https://mlsanity.com/paper/2309.07198/) (2023)

## Abstract (arXiv)

Spatial photonic Ising machines offer a novel optical platform for optimization and spin-model simulation, but existing diffraction-based schemes rely on auxiliary spins or multiplexing to encode high-rank couplings and external fields, reducing either speed or spin count. We demonstrate an amplitude-only, rank-free spatial photonic Ising machine in which arbitrary Ising Hamiltonians are encoded as Hadamard products on aligned amplitude and binary spatial modulators and read out by a single-pixel intensity measurement. The machine directly programs fully connected 797-spin Ising models with external fields at nearly 9-bit precision and operates at a constant iteration rate of ~200 Hz. By removing zero-valued product terms, the same architecture scales to sparse problems and experimentally solves a Max-Cut instance on a 424,108-vertex Mobius ladder graph. We also observe the phase transition of the Sherrington-Kirkpatrick model, demonstrating programmable optical simulation beyond low-rank couplings. These results establish amplitude modulation as a scalable route to programmable photonic Ising machines.