A sampling method combining fast Walsh-Hadamard transform and Clifford-preconditioned Monte Carlo reduces Pauli-string sampling cost from O(2^N) to O(N) with sample count independent of N for stabilizer Rényi entropies and nullity.
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In U(1)-symmetric 1D random circuits the stabilizer Rényi entropy gap closes diffusively as 1/t, with the same scaling seen in an energy-conserving Ising chain.
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Exponentially Accelerated Sampling of Pauli Strings for Nonstabilizerness
A sampling method combining fast Walsh-Hadamard transform and Clifford-preconditioned Monte Carlo reduces Pauli-string sampling cost from O(2^N) to O(N) with sample count independent of N for stabilizer Rényi entropies and nullity.
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Diffusive Dynamics of Nonstabilizerness
In U(1)-symmetric 1D random circuits the stabilizer Rényi entropy gap closes diffusively as 1/t, with the same scaling seen in an energy-conserving Ising chain.