Worldline Path Integrals for Gauge Fields and Quantum Computing

TL;DR

This paper explores the application of quantum computing algorithms to evaluate worldline path integrals in gauge fields, demonstrating promising results and methods for representing scattering processes on near-term quantum devices.

Contribution

It introduces quantum algorithms for worldline path integrals with gauge fields and demonstrates their effectiveness in classical and quantum simulations.

Findings

Quantum algorithms accurately compute path integrals in gauge fields.

Successful representation of vertex operators for scattering in quantum circuits.

Excellent agreement between quantum and classical computations.

Abstract

We study different aspects the worldline path integrals with gauge fields using quantum computing. We use the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) quantum algorithms and IBM QISKit to perform our computations. We apply these methods to the path integral of a particle moving in a Abelian and non-Abelian background gauge field associated with a constant magnetic field and the field of a chromo-magnetic field. In all cases we found excellent agreement with the classical computation. We also discuss the insertion of vertex operators into the worldline path integrals to study scattering and show how to represent them using unitary operators and quantum gates on near term quantum computers.