Statistics of topological defects across a phase transition in a digital superconducting quantum processor

TL;DR

This paper investigates the statistics of topological defects formed during quantum phase transitions in a digital superconducting quantum processor, confirming universal scaling laws and exploring the limits of the Kibble-Zurek mechanism.

Contribution

It demonstrates the universal power law scaling of higher-order cumulants of kink density across quench times in a 1D quantum Ising model on multiple quantum processors.

Findings

Higher-order cumulants follow universal power law scaling.

KZM breaks down for short quenches in finite systems.

Tensor network simulations support quantum simulation results.

Abstract

When a quantum phase transition is crossed within a finite time, critical slowing down disrupts adiabatic dynamics, resulting in the formation of topological defects. The average density of these defects scales with the quench rate, adhering to a universal power law as predicted by the Kibble-Zurek mechanism (KZM). In this study, we aim to investigate the counting statistics of kink density in the 1D transverse-field quantum Ising model. We demonstrate on multiple quantum processing units up to 100 qubits, that higher-order cumulants follow a universal power law scaling as a function of the quench time. We also show the breakdown of the KZM for short quenches for finite-size systems. Tensor network simulations corroborate our quantum simulation results for bigger systems not in the asymptotic limit.