Barren-plateau free variational quantum simulation of Z2 lattice gauge theories

TL;DR

This paper demonstrates a variational quantum eigensolver (VQE) approach for simulating Z2 lattice gauge theories, successfully capturing ground states and string breaking phenomena on quantum hardware without barren plateaus.

Contribution

It introduces a gauge-invariant VQE method for Z2 lattice gauge theories that avoids barren plateaus and is experimentally validated on IBM quantum devices.

Findings

VQE accurately finds gauge-invariant ground states.

String breaking observed on quantum hardware.

Favorable gradient scaling for larger qubit systems.

Abstract

In this work, we design a variational quantum eigensolver (VQE) suitable for investigating ground states and static string breaking in a $\mathbb{Z}_2$ lattice gauge theory (LGT). We consider a two-leg ladder lattice coupled to Kogut-Susskind staggered fermions and verify the results of the VQE simulations using tensor network methods. We find that for varying Hamiltonian parameter regimes and in the presence of external charges, the VQE is able to arrive at the gauge-invariant ground state without explicitly enforcing gauge invariance through penalty terms. Additionally, experiments showing string breaking are performed on IBM's quantum platform. Thus, VQEs are seen to be a promising tool for $\mathbb{Z}_2$ LGTs, and could pave the way for studies of other gauge groups. We find that the scaling of gradients with the number of qubits is favorable for avoiding barren plateaus. At the same time, it is not clear how to efficiently simulate the LGT using classical methods. Furthermore, strategies that avoid barren plateaus arise naturally as features of LGTs, such as choosing the initialization by setting the Gauss law sector and restricting the Hilbert space to the gauge-invariant subspace.