Log-depth circuits suffice for average-case single-copy stabilizer learning with t=O(log n), but worst-case adaptive single-copy learning requires exp(t) samples.
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An autoregressive sampler draws Pauli strings sequentially from computable conditionals to enable linear-cost fidelity estimation for random matrix product states, with a grouped commuting extension to lower variance.
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Single-copy stabilizer learning: average case and worst case
Log-depth circuits suffice for average-case single-copy stabilizer learning with t=O(log n), but worst-case adaptive single-copy learning requires exp(t) samples.
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Verifying random matrix product states with autoregressive local measurements
An autoregressive sampler draws Pauli strings sequentially from computable conditionals to enable linear-cost fidelity estimation for random matrix product states, with a grouped commuting extension to lower variance.