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 computational 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 predictions of sampling advantage without direct deployment on hardware. Although sampling of the quantum Heisenberg models studied exhibits much longer autocorrelation times on sIMs, the massively parallel sampling of hardware sIMs leads to a projected speed-up of 100 to 10000, suggesting great opportunities for studying complex quantum systems at larger scales.