Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum

Abstract

Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have emerged as a tractable means to study such dynamics. Despite generating no entanglement in the computational basis, these circuits nevertheless capture many features expected from fully quantum evolutions. In this work, we demonstrate that the differences between automaton dynamics and fully quantum dynamics are revealed by the operator entanglement spectrum, much like the entanglement spectrum of a quantum state distinguishes between the dynamics of states under Clifford and Haar random circuits. While the operator entanglement spectrum under random unitary dynamics is governed by the eigenvalue statistics of random Gaussian matrices, we show evidence that under random automaton dynamics it is described by the statistics of Bernoulli random matrices, whose entries are random variables taking values $0$ or $1$. We study the crossover between automaton and generic unitary operator dynamics as the automaton circuit is doped with gates that introduce superpositions, namely Hadamard or $R_x=e^{-i\frac{\pi }{4}X}$ gates. We find that a constant number of superposition-generating gates is sufficient to drive the operator dynamics to the random-circuit universality class, similar to earlier results on Clifford circuits doped with $T$ gates. This establishes the operator entanglement spectrum as a useful tool for probing the chaoticity and universality class of quantum dynamics.

21 pages, 13 figures. Accepted for publication in Quantum. Minor revisions in response to referee comments, including one additional figure. Formatting updated to match journal

References in corpus (35)

• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Random Quantum Circuits
• Information Scrambling in Computationally Complex Quantum Circuits
• Chaos, Complexity, and Random Matrices
• Operator space entanglement entropy in transverse Ising chain
• Many body localization and thermalization: insights from the entanglement spectrum
• Statistical distribution of quantum entanglement for a random bipartite state
• Anomalous Subdiffusion from Subsystem Symmetries
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Operator Space Entanglement Entropy in XY Spin Chains
• Random matrix techniques in quantum information theory
• Accessing scrambling using matrix product operators
• Emergent irreversibility and entanglement spectrum statistics
• Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
• Chaos and Complexity of quantum motion
• Scrambling is Necessary but Not Sufficient for Chaos
• Entanglement Complexity in Quantum Many-Body Dynamics, Thermalization and Localization
• Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
• Universal Spectral Correlations in the Chaotic Wave Function, and the Development of Quantum Chaos
• Efficient unitary designs with a system-size independent number of non-Clifford gates
• Characterizing the many-body localization transition through the entanglement spectrum
• Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
• The rank of diluted random graphs
• Quantum State Complexity in Computationally Tractable Quantum Circuits
• Evolution of entanglement spectra under generic quantum dynamics
• Mean quantum percolation
• Bridging the gap between classical and quantum many-body information dynamics
• Signatures of information scrambling in the dynamics of the entanglement spectrum
• Efficient unitary designs and pseudorandom unitaries from permutations
• Efficient Unitary T-designs from Random Sums
• Bridging Entanglement and Magic Resources within Operator Space
• Quantum and Classical Dynamics with Random Permutation Circuits

Cited by in corpus (1)

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