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Résumé |
We study the problem of irreversibility when the dynamical evolution of a
many-body system is described by a stochastic quantum circuit. In contrast to
Hamiltonian evolution, energy levels are not well defined, and the well-
established connection between the statistical fluctuations of the energy
spectrum and irreversibility cannot be made. We show that the entanglement
spectrum level statistics may provide the connection in this case. As a quantum
state initialized as a product state evolves unitarily via a random quantum
circuit, it generically gets asymptotically maximally entangled. Disentangling
the final state is a tall order without knowledge of the exact (reverse)
circuit. The entanglement spectrum level statistics, not the entanglement
entropy, can capture the difficulty of finding a disentangling circuit using a
Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-
Dyson statistics in the level spacing of the entanglement eigenvalues, and that
this is obtained from a quantum circuit made from a set of universal gates for
quantum computation. If, on the other hand, the system is evolved with a non-
universal set of gates, the statistics of the entanglement level spacing
deviates from Wigner-Dyson (e.g., Poisson distribution) and the disentangling
algorithm succeeds. |
