Quantum State Preparation for the Schwinger Model

TL;DR

This paper explores quantum algorithms for preparing states in the 1+1-dimensional Schwinger model, analyzing their convergence and gate costs to assess feasibility on near-term quantum devices.

Contribution

It compares adiabatic and QAOA algorithms for state preparation in the Schwinger model and introduces a blocked algorithm with improved scaling behavior.

Findings

QAOA and adiabatic algorithms studied for convergence and gate costs.

Blocked algorithm shows promising scaling with problem size.

Feasibility of quantum simulations depends on rapid convergence of these algorithms.

Abstract

It is not possible, using standard lattice techniques in Euclidean space, to calculate the complete fermionic spectrum of a quantum field theory. Algorithms running on quantum computers have the potential to access the theory with real-time evolution, enabling a direct computation. As a testing ground we consider the 1 + 1-dimensional Schwinger model with the presence of a {\theta} term using a staggered fermions discretization. We study the convergence properties of two different algorithms - adiabatic evolution and the Quantum Approximate Optimization Algorithm - with an emphasis on their cost in terms of CNOT gates. This is crucial to understand the feasibility of these algorithms, because calculations on near-term quantum devices depend on their rapid convergence. We also propose a blocked algorithm that has the first indications of a better scaling behavior with the dimensionality of the problem.