Universal imaginary-time critical dynamics on a quantum computer

TL;DR

This paper introduces a scalable method to study quantum critical behavior using imaginary-time evolution on quantum computers, successfully demonstrating early-time universal scaling with hardware experiments.

Contribution

It proposes a systematic approach for probing universal critical dynamics via imaginary-time evolution on quantum computers, validated through simulations and superconducting quantum hardware.

Findings

Successful extraction of universal scaling functions

First experimental demonstration on quantum hardware

Effective error mitigation confirms scaling behavior

Abstract

Quantum computers promise a highly efficient approach to investigate quantum phase transitions, which describe abrupt changes between different ground states of many-body systems. At quantum critical points, the divergent correlation length and entanglement entropy render the ground state preparation difficult. In this work, we explore the imaginary-time evolution for probing the universal critical behavior as the universal information of the ground state can be extracted in the early-time relaxation process. We propose a systematic and scalable scheme to probe the universal behaviors via imaginary-time critical dynamics on quantum computers and demonstrate the validness of our approach by both numerical simulation and quantum hardware experiments. With the full form of the universal scaling function in terms of imaginary time, system size, and circuit depth, we successfully probe the universality by scaling analysis of the critical dynamics at an early time and with shallower quantum circuit depth. Equipped with quantum error mitigation, we also confirm the expected scaling behavior from experimental results on a superconducting quantum processor which stands as the first experimental demonstration on universal imaginary-time quantum critical dynamics.