Many Body Thermodynamics on Quantum Computers via Partition Function Zeros

TL;DR

This paper demonstrates how to analyze phase transitions in quantum systems by calculating partition function zeros on noisy quantum computers, providing a scalable approach to study critical phenomena beyond classical capabilities.

Contribution

It introduces a robust method for computing partition function zeros on intermediate-scale quantum computers, enabling the study of critical phenomena in complex quantum systems.

Findings

Successfully performed partition function zeros analysis on trapped ion quantum computers.

Demonstrated the transition from XY-like to Ising-like behavior in the XXZ model.

Outlined a pathway for future large-scale quantum simulations of critical phenomena.

Abstract

Interacting quantum systems illustrate complex phenomena including phase transitions to novel ordered phases. The universal nature of critical phenomena reduces their description to determining only the transition temperature and the critical exponents. Numerically calculating these results for systems in new universality classes is complicated due to critical slowing down, requiring increasing resources near the critical point. An alternative approach analytically continues the calculation onto the complex plane and determines the partition function via its zeros. Here we show how to robustly perform this analysis on noisy intermediate scale trapped ion quantum computers in a scalable manner, using the XXZ model as a prototype. We illustrate the transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the determination of critical phenomena for systems that cannot be solved otherwise.