Stabilizer testing requires Θ(n-k) copies and non-adaptive learning Θ(n²/k) copies with k-qubit memory, removing the testing-learning separation.
Gong , author J
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A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
CBNE enables estimation of nonlinear quantum properties such as higher-order expectations from a single randomized measurement setting under sufficient system dimension or ancillary qubits.
citing papers explorer
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Optimal Stabilizer Testing and Learning with Limited Quantum Memory
Stabilizer testing requires Θ(n-k) copies and non-adaptive learning Θ(n²/k) copies with k-qubit memory, removing the testing-learning separation.
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Quantum Time Lower Bounds by Permutation Invariance
A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
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Quantum Nonlinear Properties from a Single Measurement Setting
CBNE enables estimation of nonlinear quantum properties such as higher-order expectations from a single randomized measurement setting under sufficient system dimension or ancillary qubits.