Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator

Understanding how hydrodynamic behaviour emerges from the unitary evolution of many-particle Schr\"odinger equation is a central goal non-equilibrium statistical mechanics. In this work we implement digital simulation discrete time quantum dynamics spin-$\frac{1}{2}$ XXZ spin chain on noisy near-term device, and extract high temperature transport exponent at isotropic point. We simulate temporal decay relevant correlation function using pseudo-random state generated by random circuit that specifically tailored to ibmq-montreal $27$ qubit device. The resulting output excitation highly inhomogeneous background. From subsequent device are able an anomalous super-diffusive consistent with conjectured Kardar-Parisi-Zhang (KPZ) scaling Furthermore restoration diffusion application integrability breaking potential.