Enhancing Variational Quantum Eigensolvers for SU(2) Lattice Gauge Theory via Systematic State Preparation

TL;DR

This paper improves variational quantum eigensolvers for SU(2) lattice gauge theories by developing a systematic, gauge-invariant state preparation method suitable for near-term quantum devices, demonstrated on a minimal toy model.

Contribution

It introduces a systematic gauge-invariant state preparation ansatz that mitigates barren plateaus and scales advantages using a spin-network basis for non-Abelian gauge theories.

Findings

Effective in creating gauge-invariant excitations

Reduces barren plateau issues in variational algorithms

Demonstrated robustness under simulated quantum noise

Abstract

Computing the vacuum and energy spectrum in non-Abelian, interacting lattice gauge theories remains an open challenge, in part because approximating the continuum limit requires large lattices and huge Hilbert spaces. To address this difficulty with near-term quantum computing devices, we adapt the variational quantum eigensolver to non-Abelian gauge theories. We outline scaling advantages when using a spin-network basis to simulate the gauge-invariant Hilbert space and develop a systematic state preparation ansatz that creates gauge-invariant excitations while alleviating the barren plateau problem. We illustrate our method in the context of SU(2) Yang-Mills theory by testing it on a minimal toy model consisting of a single vertex in 3+1 dimensions. In this toy model, simulations allow us to investigate the impact of noise expected in current quantum devices.