Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model

TL;DR

This paper investigates the dynamics of noise-averaged operators in coupled qubits, revealing connections to classical stochastic models and the Fredrickson-Andersen model, with conjectures about fluctuation universality classes in higher dimensions.

Contribution

It establishes mappings from noisy quantum spin systems to classical stochastic models and explores the universality of fluctuation behavior in operator spreading.

Findings

Operator dynamics show diffusive or exponential relaxation depending on drive conservation.

The second moment of operators maps to the Fredrickson-Andersen model.

Numerical evidence suggests 2D fluctuations are in the KPZ universality class.

Abstract

We study noise-averaged observables for a system of exchange-coupled quantum spins (qubits), each subject to a stochastic drive, by establishing mappings onto stochastic models in the strong-noise limit. Averaging over noise yields Lindbladian equations of motion; when these are subjected to a strong-noise perturbative treatment, classical master equations are found to emerge. The dynamics of noise averages of operators displays diffusive behaviour or exponential relaxation, depending on whether the drive conserves one of the spin components or not. In the latter case, the second moment of operators -- from which the average subsystem purity and out-of-time-order correlation functions can be extracted -- is described by the Fredrickson-Andersen model, originally introduced as a model of cooperative relaxation near the glass transition. It is known that fluctuations of a ballistically propagating front in the model are asymptotically Gaussian in one dimension. We extend this by conjecturing, with strong numerical evidence, that in two dimensions the long-time fluctuations are in the Kardar-Parisi-Zhang universality class, complementing a similar observation in random unitary circuits.