Quantum Simulation of Finite Temperature Schwinger Model via Quantum Imaginary Time Evolution

TL;DR

This paper demonstrates a quantum-classical hybrid approach using Quantum Imaginary Time Evolution to simulate the finite-temperature Schwinger model, effectively addressing challenges in thermal state preparation and avoiding the sign problem.

Contribution

The study introduces a novel quantum algorithm combining TPQ states and QITE for finite-temperature quantum field theory simulations, overcoming limitations of traditional methods.

Findings

Successfully computed the chiral condensate in the massless model, matching analytical results.

Simulated the massive model with a non-zero topological term, revealing temperature and theta dependence.

Method remains effective at non-zero theta, unlike conventional lattice Monte Carlo approaches.

Abstract

We study the Schwinger model at finite-temperature regime using a quantum-classical hybrid algorithm. The preparation of thermal state on quantum circuit presents significant challenges. To address this, we adopt the Thermal Pure Quantum (TPQ) state approach and apply the Quantum Imaginary Time Evolution (QITE) algorithm to implement the necessary imaginary time evolution. We first compute the chiral condensate in the massless Schwinger model, verifying its consistency with the analytical solution. We then simulate the massive Schwinger model with non-zero topological $\theta$-term to investigate the temperature and $\theta$-dependence of the chiral condensate. Our method works well even at non-zero $\theta$ regime, while the conventional lattice Monte Carlo method suffers from the sign problem in this system.