Fermion determinants on a quantum computer

TL;DR

This paper introduces a quantum algorithm for efficiently computing the logarithm of fermion matrix determinants, leveraging quantum eigenvalue transform and mean estimation, with favorable scaling in matrix size.

Contribution

The paper proposes a novel quantum algorithm for determinant calculation of fermion matrices, improving computational efficiency over classical methods.

Findings

Query complexity scales as O(V log V) with matrix dimension V.

Uses quantum eigenvalue transform and quantum mean estimation techniques.

Provides a quantum approach to a fundamental problem in lattice gauge theories.

Abstract

We present a quantum algorithm to compute the logarithm of the determinant of the fermion matrix, assuming access to a classical lattice gauge field configuration. The algorithm uses the quantum eigenvalue transform, and quantum mean estimation, giving a query complexity that scales like $O(V\log(V))$ in the matrix dimension $V$.