Derives improved mode-independent sample complexity bounds O(η log η) for fermionic classical shadows on particle-preserving operators and Slater determinant overlaps.
Operator growth in random quantum circuits with symmetry
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abstract
We study random quantum circuits with symmetry, where the local 2-site unitaries are drawn from a quotient or subgroup of the full unitary group $U(d)$. Random quantum circuits are minimal models of local quantum chaotic dynamics and can be used to study operator growth and the emergence of diffusive hydrodynamics. We derive the transition probabilities for the stochastic process governing the growth of operators in four classes of symmetric random circuits. We then compute the butterfly velocities and diffusion constants for a spreading operator by solving a simple random walk in each class of circuits.
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Random circuits with orthogonal or symplectic symmetry exhibit ternary Pauli weights, finite-width domain walls, and component-dependent butterfly velocities that can exceed the Haar value for q=2.
In the thermodynamic limit the quantum and classical full-counting statistics of charge coincide exactly with no finite-time corrections, while the averaged von Neumann entanglement entropy admits a fully explicit expression obtained from the Jacobi-process dynamics of correlation-matrix eigenvalues
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