Quantum computing of semiclassical formulas

TL;DR

This paper demonstrates that quantum computers can efficiently implement semiclassical formulas like the Gutzwiller trace formula, offering quadratic or greater computational advantages over classical methods.

Contribution

It introduces explicit quantum algorithms to compute classical trajectories and test semiclassical approximations, enhancing computational efficiency in quantum simulations.

Findings

Quantum algorithms outperform classical methods in computing semiclassical formulas.

The computational gain is generally quadratic, with potential for larger improvements.

Quantum approaches enable testing semiclassical approximations via quantum evolution.

Abstract

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.