Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model

TL;DR

This paper demonstrates a self-verifying hybrid quantum-classical approach to simulate the lattice Schwinger model, enabling study of complex gauge theories without direct Hamiltonian realization in the lab.

Contribution

It introduces a self-verifying variational quantum simulation method using a trapped-ion quantum processor for lattice gauge theories, bypassing the need for analog Hamiltonian implementation.

Findings

Successfully simulated the ground state and energy gaps of the Schwinger model.

Provided algorithmic error bars for energy measurements.

Demonstrated the method's applicability to intractable models.

Abstract

Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments demonstrating self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics. Contrary to analog quantum simulation, this approach forgoes the requirement of realising the targeted Hamiltonian directly in the laboratory, thus allowing the study of a wide variety of previously intractable target models. Here, we focus on the Lattice Schwinger model, a gauge theory of 1D quantum electrodynamics. Our quantum co-processor is a programmable, trapped-ion analog quantum simulator with up to 20 qubits, capable of generating families of entangled trial states respecting symmetries of the target Hamiltonian. We determine ground states, energy gaps and, by measuring variances of the Schwinger Hamiltonian, we provide algorithmic error bars for energies, thus addressing the long-standing challenge of verifying quantum simulation.