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

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.

11 pages, 7 figures. Accepted version

References in corpus (14)

• Black holes as mirrors: quantum information in random subsystems
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Emergent statistical mechanics of entanglement in random unitary circuits
• Slow scrambling in disordered quantum systems
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
• Macroscopic Facilitation of Glassy Relaxation Kinetics: Ultra Stable Glass Films with Front-Like Thermal Response
• Exact convergence times for generation of random bipartite entanglement
• Emergence of typical entanglement in two-party random processes
• Fast scrambling on sparse graphs
• Localization with random time-periodic quantum circuits
• Entanglement production and information scrambling in a noisy spin system
• Optimal two-qubit gate for generation of random bipartite entanglement
• Constraints on hydrodynamics from many-body quantum chaos

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