Predicting sampling advantage of stochastic Ising Machines for Quantum Simulations

Stochastic Ising machines, sIMs, are highly promising accelerators for optimization and sampling of computational problems that can be formulated as an Ising model. Here we investigate the computational advantage of sIM for simulations of quantum magnets with neural-network quantum states (NQS), in which the quantum many-body wave function is mapped onto an Ising model. We study the sampling performance of sIM for NQS by comparing sampling on a software-emulated sIM with standard Metropolis-Hastings sampling for NQS. We quantify the sampling efficiency by the number of steps required to reach iso-accurate stochastic estimation of the variational energy and show that this is entirely determined by the autocorrelation time of the sampling. This enables predications of sampling advantage without direct deployment on hardware. For the quantum Heisenberg models studied and experimental results on the runtime of sIMs, we project a possible speed-up of 100 to 10000, suggesting great opportunities for studying complex quantum systems at larger scales.