Understanding how hydrodynamic behaviour emerges from the unitary evolution of the many-particle Schr\"odinger equation is a central goal of non-equilibrium statistical mechanics. In this work we implement a digital simulation of the discrete time quantum dynamics of a spin-21 XXZ spin chain on a noisy near-term quantum device, and we extract the high temperature transport exponent at the isotropic point. We simulate the temporal decay of the relevant spin correlation function at high temperature using a pseudo-random state generated by a random circuit that is specifically tailored to the ibmq-montreal 27 qubit device. The resulting output is a spin excitation on a highly inhomogeneous background. From the subsequent discrete time dynamics on the device we are able to extract an anomalous super-diffusive exponent consistent with the conjectured Kardar-Parisi-Zhang (KPZ) scaling at the isotropic point. Furthermore we simulate the restoration of spin diffusion with the application of an integrability breaking potential.
@article{arxiv.2208.12243,
title = {Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator},
author = {Nathan Keenan and Niall Robertson and Tara Murphy and Sergiy Zhuk and John Goold},
journal= {arXiv preprint arXiv:2208.12243},
year = {2023}
}