Toward Quantum Simulations of $\mathbb{Z}_2$ Gauge Theory Without State Preparation

TL;DR

This paper introduces a method combining classical sampling and projection operators to compute matrix elements in lattice gauge theories on quantum computers without the need for explicit state preparation, demonstrated on 2+1d $ ext{Z}_2$ gauge theory.

Contribution

It presents a novel approach that reduces quantum resource requirements by avoiding explicit state preparation in simulating lattice gauge theories.

Findings

Successfully computed Minkowski matrix elements using the proposed method.

Demonstrated the approach on small lattices with a quantum simulator.

Showed potential for scalable quantum simulations of gauge theories.

Abstract

Preparing strongly-coupled particle states on quantum computers requires large resources. In this work, we show how classical sampling coupled with projection operators can be used to compute Minkowski matrix elements without explicitly preparing these states on the quantum computer. We demonstrate this for the 2+1d $\mathbb{Z}_2$ lattice gauge theory on small lattices with a quantum simulator.