Accelerated quantum circuit Monte Carlo simulation for heavy quark thermalization

Thermalization of heavy quarks in the quark-gluon plasma is one of the most promising phenomena for understanding the strong interaction. The energy loss and momentum broadening at low momentum can be well described by a stochastic process with drag and diffusion terms. Recent advances in quantum computing, in particular, quantum amplitude estimation (QAE), promise to provide a quadratic speedup in simulating stochastic processes. We introduce and formalize an accelerated quantum circuit Monte Carlo (aQCMC) framework to simulate heavy quark thermalization. With simplified drag and diffusion coefficients connected by Einstein’s relation, we simulate the thermalization of a heavy quark in isotropic and anisotropic mediums using an ideal quantum simulator and compare that to thermal expectations. With Grover-like QAE, we calculate physical observables with quadratically fewer resources, which is a boost over the classical MC simulation that usually requires a large sampling number at the same estimation accuracy.