  Thermalization of heavy quarks in the quark-gluon plasma (QGP) 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 speed-up 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.
