Growth and spreading of quantum resources under random circuit dynamics

TL;DR

This paper investigates how quantum resources like magic, coherence, and non-Gaussianity evolve and spread in one-dimensional qubit chains under random circuit dynamics, revealing universal behaviors and resource spreading mechanisms.

Contribution

It provides a unified analysis of the dynamics and spreading of various quantum resources in local random circuits, highlighting universal patterns and scaling laws.

Findings

Resource peaks scale logarithmically with subsystem size.

Resources decay as subsystems approach maximally mixed states.

Ballistic spreading of resources occurs in entangling circuits.

Abstract

Quantum many-body dynamics generate nonclassical correlations naturally described by quantum resource theories. Quantum magic resources (or nonstabilizerness) capture deviation from classically simulable stabilizer states, while coherence and fermionic non-Gaussianity measure departure from the computational basis and from fermionic Gaussian states, respectively. We track these resources in a subsystem of a one-dimensional qubit chain evolved by random brickwall circuits. For resource-generating gates, evolution from low-resource states exhibits a universal rise-peak-fall behavior, with the peak time scaling logarithmically with subsystem size and the resource eventually decaying as the subsystem approaches a maximally mixed state. Circuits whose gates do not create the resource but entangle neighboring qubits, give rise to a ballistic spreading of quantum resource initially confined to a region of the initial state. Our results give a unified picture of spatiotemporal resource dynamics in local circuits and a baseline for more structured quantum many-body systems.