Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state for rotated bases.
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Conjecture that the Hausdorff dimension of the frontier of the SFF random walk approaches 4/3 for chaotic Hamiltonians and 1 for integrable ones, with proofs of Gaussian statistics under Lyapunov conditions on degeneracies and exact moments for unequal-step walks.
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Rise and fall of nonstabilizerness via random measurements
Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state for rotated bases.
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Integrability and Chaos via fractal analysis of Spectral Form Factors: Gaussian approximations and exact results
Conjecture that the Hausdorff dimension of the frontier of the SFF random walk approaches 4/3 for chaotic Hamiltonians and 1 for integrable ones, with proofs of Gaussian statistics under Lyapunov conditions on degeneracies and exact moments for unequal-step walks.