Digital Quantum Simulation for Spectroscopy of Schwinger Model

TL;DR

This paper introduces a digital quantum simulation method using coherent imaging spectroscopy to compute energy spectra of quantum field theories, demonstrated on the Schwinger model, highlighting potential efficiency on future quantum computers.

Contribution

It presents a novel quantum algorithm for spectroscopy of quantum field theories and applies it to the Schwinger model, including practical simulation techniques and complexity analysis.

Findings

Successful application of the algorithm to the Schwinger model on a classical simulator.

Analysis of quench types and their effects on simulation results.

Estimation of the method's efficiency for fault-tolerant quantum computers.

Abstract

This note discusses a method for computing the energy spectra of quantum field theory utilizing digital quantum simulation. A quantum algorithm, called coherent imaging spectroscopy, quenches the vacuum with a time-oscillating perturbation and then reads off the excited energy levels from the loss in the vacuum-to-vacuum probability following the quench. As a practical demonstration, we apply this algorithm to the (1+1)-dimensional quantum electrodynamics with a topological term known as the Schwinger model, where the conventional Monte Carlo approach is practically inaccessible. In particular, on a classical simulator, we prepare the vacuum of the Schwinger model on a lattice by adiabatic state preparation and then apply various types of quenches to the approximate vacuum through Suzuki-Trotter time evolution. We discuss the dependence of the simulation results on the specific types of quenches and introduce various consistency checks, including the exact diagonalization and the continuum limit extrapolation. The estimation of the computational complexity required to obtain physically reasonable results implies that the method is likely efficient in the coming era of early fault-tolerant quantum computers.