Quantum simulation of the Schwinger model: A study of feasibility

TL;DR

This paper investigates the practical feasibility of quantum simulation for the Schwinger model, focusing on gauge representation, adiabatic state preparation, and effects of noise, demonstrating promising results for small systems.

Contribution

It provides a numerical analysis of finite-dimensional gauge representations and their convergence, and assesses the robustness of quantum simulations under realistic conditions.

Findings

Finite-dimensional gauge representations converge rapidly.

Adiabatic vacuum preparation time is system-size independent.

Low noise levels allow accurate ground-state measurements despite gauge symmetry violations.

Abstract

We analyze some crucial questions regarding the practical feasibility of quantum simulation for lattice gauge models. Our analysis focuses on two models suitable for the quantum simulation of the Schwinger Hamiltonian, or QED in 1+1 dimensions, which we investigate numerically using tensor networks. In particular, we explore the effect of representing the gauge degrees of freedom with finite-dimensional systems and show that the results converge rapidly; thus even with small dimensions it is possible to obtain a reasonable accuracy. We also discuss the time scales required for the adiabatic preparation of the interacting vacuum state and observe that for a suitable ramping of the interaction the required time is almost insensitive to the system size and the dimension of the physical systems. Finally, we address the possible presence of noninvariant terms in the Hamiltonian that is realized in the experiment and show that for low levels of noise it is still possible to achieve a good precision for some ground-state observables, even if the gauge symmetry is not exact in the implemented model.