Gauge invariant quantum circuits for $U(1)$ and Yang-Mills lattice gauge theories

TL;DR

This paper introduces gauge-invariant parametrized quantum circuits for $U(1)$ and Yang-Mills lattice gauge theories, ensuring physical constraints are maintained during variational calculations and real-time dynamics, thus improving quantum simulation efficiency.

Contribution

It proposes a new class of compact, flexible quantum circuits that inherently preserve gauge invariance, enabling more reliable and resource-efficient simulations of lattice gauge theories.

Findings

Circuits preserve gauge invariance during optimization.

They enable accurate ground state and dynamical property calculations.

Resource requirements are significantly reduced for real-time dynamics.

Abstract

Quantum computation represents an emerging framework to solve lattice gauge theories (LGT) with arbitrary gauge groups, a general and long-standing problem in computational physics. While quantum computers may encode LGT using only polynomially increasing resources, a major openissue concerns the violation of gauge-invariance during the dynamics and the search for groundstates. Here, we propose a new class of parametrized quantum circuits that can represent states belonging only to the physical sector of the total Hilbert space. This class of circuits is compact yet flexible enough to be used as a variational ansatz to study ground state properties, as well as representing states originating from a real-time dynamics. Concerning the first application, the structure of the wavefunction ansatz guarantees the preservation of physical constraints such as the Gauss law along the entire optimization process, enabling reliable variational calculations. As for the second application, this class of quantum circuits can be used in combination with timedependent variational quantum algorithms, thus drastically reducing the resource requirements to access dynamical properties.