Quantum simulation of non-equilibrium dynamics and thermalization in the Schwinger model

TL;DR

This paper demonstrates how digital quantum computers can simulate the non-equilibrium dynamics and thermalization processes of the Schwinger model, a fundamental quantum field theory, by treating it as an open quantum system.

Contribution

It introduces a method to simulate the Schwinger model's real-time dynamics and thermal state preparation using quantum computers, incorporating environmental effects via Lindblad equations.

Findings

Successful simulation of non-equilibrium dynamics on IBM quantum devices

Thermalization process observed through open quantum system approach

Framework applicable to other quantum field theories and quantum technologies

Abstract

We present simulations of non-equilibrium dynamics of quantum field theories on digital quantum computers. As a representative example, we consider the Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a Yukawa-type interaction to a thermal environment described by a scalar field theory. We use the Hamiltonian formulation of the Schwinger model discretized on a spatial lattice. With the thermal scalar fields traced out, the Schwinger model can be treated as an open quantum system and its real-time dynamics are governed by a Lindblad equation in the Markovian limit. The interaction with the environment ultimately drives the system to thermal equilibrium. In the quantum Brownian motion limit, the Lindblad equation is related to a field theoretical Caldeira-Leggett equation. By using the Stinespring dilation theorem with ancillary qubits, we perform studies of both the non-equilibrium dynamics and the preparation of a thermal state in the Schwinger model using IBM's simulator and quantum devices. The real-time dynamics of field theories as open quantum systems and the thermal state preparation studied here are relevant for a variety of applications in nuclear and particle physics, quantum information and cosmology.