Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods

TL;DR

This paper demonstrates the use of variational quantum algorithms, specifically VQE, to prepare the vacuum state of SU(3) lattice Yang-Mills theories on quantum hardware, exploring optimization methods and scalable ansatz construction.

Contribution

It introduces a scalable ansatz for SU(3) lattice gauge theories and applies VQE to small systems on real quantum hardware, advancing quantum simulation of gauge theories.

Findings

VQE successfully prepared vacuum states for SU(3) on small systems.

Bayesian optimization and gradient descent were effective for classical optimization.

Scalable ansatz construction was demonstrated using domain decomposition.

Abstract

Studying QCD and other gauge theories on quantum hardware requires the preparation of physically interesting states. The Variational Quantum Eigensolver (VQE) provides a way of performing vacuum state preparation on quantum hardware. In this work, VQE is applied to pure SU(3) lattice Yang-Mills on a single plaquette and one dimensional plaquette chains. Bayesian optimization and gradient descent were investigated for performing the classical optimization. Ansatz states for plaquette chains are constructed in a scalable manner from smaller systems using domain decomposition and a stitching procedure analogous to the Density Matrix Renormalization Group (DMRG). Small examples are performed on IBM's superconducting Manila processor.