Measuring Butterfly Velocity in the XY Model on Emerging Quantum Computers

TL;DR

This paper introduces a quantum teleportation-based protocol and Riemannian Trust-Region method to measure butterfly velocity in the XY model, demonstrating its feasibility on NISQ devices and aligning with analytical results.

Contribution

It presents a novel quantum algorithmic approach to estimate butterfly velocity, applicable to complex lattice models on emerging quantum computers.

Findings

Agreement between numerical simulations and analytical calculations

Successful demonstration on NISQ devices

Potential for studying complex quantum systems

Abstract

The butterfly velocity is commonly used to understand information transport properties in quantum dynamical systems and is related to growth of operators. Here we utilise a quantum teleportation based protocol and Riemannian Trust-Region method to estimate the butterfly velocity via the operator averaged out-of-time-order correlation function. We particularly study the XY model and analytically find the maximum group velocity. We then report a proof-of-concept demonstration of this method to estimate the butterfly velocity on NISQ-devices. The numerical simulation results obtained here are compared with our analytical calculations and found to be in agreement. The quantum algorithmic methods presented here can be more generally utilised to study information transport properties in more complicated lattice models.