A virtually connected probabilistic computer as a solver for higher-order, densely connected, or reconfigurable combinatorial optimisation problems

TL;DR

This paper explores a novel probabilistic computing architecture using virtual connections and photonic quantum generators to efficiently solve complex combinatorial problems that are challenging for traditional hardware.

Contribution

It introduces the concept of virtually connected hardware with heuristic methods and graph coloring for scalable, high-quality solutions to geometrically constrained problems.

Findings

Photonic probabilistic computer outperforms digital annealing in solving Erdos-Renyi graph spin-glasses.

Virtual hardware connections mitigate topological restrictions in problem geometries.

Simulations predict significant speedups over existing solution methods.

Abstract

Recently, there has been growing interest in unconventional computing as an approach for solving NP-hard problems, by developing dedicated hardware to find solutions more efficiently than conventional CPUs. In many of these approaches, however, certain problem geometries must be transformed into forms that are more amenable to the available hardware topology through techniques such as embedding, sparsification, and quadratisation, leading to a deterioration in solution quality. A probabilistic computing architecture based on high speed photonic quantum random number generators was recently proposed which utilises virtual hardware connections (Aboushelbaya et al., 2025), circumventing the necessity for such procedures. Here, we discuss the applicability of virtually connected hardware for running heuristic solving methods to solve a selection of problems, which due to their geometry, would suffer from topological hardware restrictions. We also employ greedy graph colouring algorithms for hardware parallelisation, allowing favourable scaling for desirable solution qualities. To emphasise the difficulty in solving these problems on physically connected hardware, we demonstrate the increase in problem size that would occur with quadratisation or sparsification. Using simulations to emulate hardware, we predict that a photonic probabilistic computer would outperform the time to solution recently reported for digital annealing units, on the ground state approximation of Erdos-Renyi graph spin-glasses, by orders of magnitude.