Quantum computing of the pairing Hamiltonian at finite temperatures

TL;DR

This paper demonstrates the use of quantum computing to simulate the pairing Hamiltonian at finite temperatures, showing accurate results and phase transition behavior in a four-particle system.

Contribution

It introduces a quantum simulation approach for the pairing Hamiltonian at finite temperatures using variational quantum algorithms and error mitigation techniques.

Findings

Quantum simulations closely match exact solutions at high temperatures.

The method captures the superfluid-normal phase transition.

Error mitigation improves noisy quantum computation results.

Abstract

In this work, we study the pairing Hamiltonian with four particles at finite temperatures on a quantum simulator and a superconducting quantum computer. The excited states are obtained by the variational quantum deflation (VQD). The error-mitigation methods are applied to improve the noisy results. The simulation of thermal excitation states is performed using the same variational circuit as at zero temperature. The results from quantum computing become close to exact solutions at high temperatures, and demonstrate a smooth superfluid-normal phase transition as a function of temperatures as expected in finite systems.