Two-step phantom relaxation of out-of-time-ordered correlations in random circuits

Abstract

We study out-of-time-ordered correlation (OTOC) functions in various random quantum circuits and show that the average dynamics is governed by a Markovian propagator. This is then used to study relaxation of OTOC to its long-time average value in circuits with random single-qubit unitaries, finding that relaxation in general proceeds in two steps: in the first phase that lasts upto an extensively long time the relaxation rate is given by a phantom eigenvalue of a non-symmetric propagator, whereas in the second phase the rate is determined by the true 2nd largest propagator eigenvalue. We also obtain exact OTOC dynamics on the light-cone and an expression for the average OTOC in finite random circuits with random two-qubit gates.

17 pages

References in corpus (8)

• Black holes as mirrors: quantum information in random subsystems
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Scrambling in Random Unitary Circuits: Exact Results
• Exact convergence times for generation of random bipartite entanglement
• Emergence of typical entanglement in two-party random processes
• Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
• Optimal two-qubit gate for generation of random bipartite entanglement
• Universal scrambling in gapless quantum spin chains

Cited by in corpus (16)

• Solvable model of deep thermalization with distinct design times
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• From Dual Unitarity to Generic Quantum Operator Spreading
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Unraveling the emergence of quantum state designs in systems with symmetry
• Purity decay rate in random circuits with different configurations of gates
• Two-step relaxation in local many-body Floquet systems
• Theory of Irreversibility in Quantum Many-Body Systems
• Information Scrambling and the Correspondence of Entanglement- and Operator Dynamics in Systems with Nonlocal Interactions
• Universal Time-Entanglement Trade-off in Open Quantum Systems
• Manipulating the Relaxation Time of Boundary-Dissipative Systems through Bond Dissipation
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
• Boom and bust cycles due to pseudospectra of matrices with unimodular spectra
• More global randomness from less-random local gates