Classically emulated digital quantum simulation of the Schwinger model with a topological term via adiabatic state preparation

Abstract

We designed a protocol for digital quantum computation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on 1+1 dimensional quantum electrodynamics with the θ term known as the Schwinger model and test our protocol for this on an IBM simulator. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in the massless case agrees with the known exact result. In the massive case, we find an agreement with mass perturbation theory in the small-mass regime and deviations in the large-mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation appears a promising tool to explore nonperturbative aspects of gauge theories with real time and topological terms.

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