Expectations from the Liouville-von Neumann Equation Using Chebyshev Expansion

TL;DR

The paper introduces an efficient dimension reduction method for solving the Liouville-von Neumann equation in quantum systems using Chebyshev polynomial expansion, enabling accurate expectation value calculations.

Contribution

It presents a novel Chebyshev expansion-based technique for dimension reduction in quantum dynamics, preserving information and improving computational efficiency.

Findings

Method is highly efficient for quantum expectation calculations.

Demonstrated effectiveness on a model quantum problem.

Outperforms some existing alternative approaches.

Abstract

We consider a natural dimension reduction technique for the Liouville-von Neumann equation for a mixed quantum system based on evaluation of a trace formula combined with a direct expansion in modified Chebyshev polynomials. This reduction is highly efficient and does not destroy any information. We demonstrate the practical application of the scheme with a model problem and compare with popular alternatives. This method can be applied to autonomous quantum problems where the desired outcome of quantum simulation is the expectation of an observable.