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.