Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom

Abstract

We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process and proved that there are large spectral equivalence classes -- different configurations have the same spectrum. Optimal gates and the protocol that generate entanglement with the fastest theoretically possible rate are identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which is a consequence of non-Hermiticity. In particular, non-Hermiticity can cause the rate to be either faster, or, even more interestingly, slower than predicted by the matrix eigenvalue gap. This is caused by an exponential in system size explosion of expansion coefficient sizes resulting in a 'phantom' eigenvalue, and is due to non-orthogonality of non-Hermitian eigenvectors. We numerically demonstrate that the phenomenon occurs also in random circuits with non-optimal generic gates, random U(4) gates, and also without spatial or temporal randomness, suggesting that it could be of wide importance also in other non-Hermitian settings, including correlations.

22 pages; v2: 27 pages, new data on generic gates, Haar random gates, and on fluctuations and non-random systems

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Cited by in corpus (29)

• Solvable model of deep thermalization with distinct design times
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• Correlations and commuting transfer matrices in integrable unitary circuits
• Symmetrized Liouvillian Gap in Markovian Open Quantum Systems
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Exponentially-enhanced Quantum Non-Hermitian Sensing via Optimized Coherent Drive
• Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
• Metastability associated with many-body explosion of eigenmode expansion coefficients
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
• Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
• Exponential sensitivity revival of noisy non-Hermitian quantum sensing with two-photon drives
• Macroscopic effects of localised measurements in jammed states of quantum spin chains
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Two-step relaxation in local many-body Floquet systems
• Purity decay rate in random circuits with different configurations of gates
• Theory of Irreversibility in Quantum Many-Body Systems
• Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling
• Universal Time-Entanglement Trade-off in Open Quantum Systems
• Localization and integrability breaking in weakly interacting Floquet circuits
• Integrability is generic in homogeneous U(1)-invariant nearest-neighbor qubit circuits
• Oscillating-mode gap: an indicator of phase transition in open quantum many-body systems
• Entangling power, gate typicality, and measurement-induced phase transitions
• Classification of same-gate quantum circuits and their space-time symmetries with application to the level-spacing distribution
• Dual-unitary shadow tomography
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Boom and bust cycles due to pseudospectra of matrices with unimodular spectra
• Time Glasses: Symmetry Broken Chaotic Phase with a Finite Gap
• More global randomness from less-random local gates