Accelerated quantum circuit Monte-Carlo simulation for heavy quark thermalization

TL;DR

This paper introduces an accelerated quantum circuit Monte-Carlo framework utilizing quantum amplitude estimation to efficiently simulate heavy quark thermalization in quark-gluon plasma, achieving quadratic speed-up over classical methods.

Contribution

The paper formalizes a novel quantum Monte-Carlo approach for simulating heavy quark thermalization, leveraging quantum amplitude estimation for resource-efficient computation.

Findings

Quantum simulation matches thermal expectations for heavy quarks.

Quadratic reduction in resources needed for observable calculations.

Effective simulation in both isotropic and anisotropic mediums.

Abstract

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.