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.

翻译：近年来，非常规计算作为解决NP难问题的方法日益受到关注，其通过开发专用硬件以比传统CPU更高效地寻找解决方案。然而，许多此类方法需通过嵌入、稀疏化和二次化等技术，将特定问题几何结构转化为更适配现有硬件拓扑的形式，这会导致解质量的下降。近期提出了一种基于高速光子量子随机数生成器的概率计算架构，该架构利用虚拟硬件连接（Aboushelbaya等人，2025），从而规避了此类处理步骤的必要性。本文探讨了虚拟连接硬件在运行启发式求解方法以解决若干问题时的适用性——这些问题由于其几何特性，将受限于拓扑硬件约束。我们还采用贪心图着色算法实现硬件并行化，使得在理想解质量下实现有利的规模扩展。为凸显在物理连接硬件上求解此类问题的难度，我们展示了二次化或稀疏化所导致的问题规模增长。通过模拟仿真硬件环境，我们预测光子概率计算机在求解厄尔多斯-雷尼图自旋玻璃基态近似问题时，其求解时间将比近期报道的数字退火单元快数个数量级。