Adiabatic state preparation for digital quantum simulations of QED in 1 + 1D

TL;DR

This paper investigates adiabatic state preparation methods for digital quantum simulations of 1+1D QED, identifying issues with existing procedures and proposing a new Hamiltonian to improve ground state preparation, especially with topological effects.

Contribution

The authors identify limitations of current adiabatic algorithms in simulating 1+1D QED and introduce a new Hamiltonian that enhances the accuracy of ground state preparation in the presence of topological terms.

Findings

Existing adiabatic procedures encounter level crossing issues.

The new Hamiltonian improves ground state targeting.

Effective simulation of string breaking phenomena.

Abstract

Quantum electrodynamics in 1 + 1D (QED2) shares intriguing properties with QCD, including confinement, string breaking, and interesting phase diagram when the non-trivial topological $\theta$-term is considered. Its lattice regularization is a commonly used toy model for quantum simulations of gauge theories on near-term quantum devices. In this work, we address algorithms for adiabatic state preparation in digital quantum simulations of QED2. We demonstrate that, for specific choices of parameters, the existing adiabatic procedure leads to level crossing between states of different charge sectors, preventing the correct preparation of the ground state. We further propose a new adiabatic Hamiltonian and verify its efficiency in targeting systems with a nonzero topological $\theta$-term and in studying string breaking phenomena.