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.
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Embedding experimental quantum states into high-distance codes enables exponential speedups in fault-tolerant shadow tomography and cubic observable estimation over unencoded adaptive strategies.
Exact replica threshold for tr(ρ^t) is ⌈t/2⌉, with fewer replicas incurring dimension-dependent sample complexity.
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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.
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Exponential speedups in fault-tolerant processing of quantum experiments
Embedding experimental quantum states into high-distance codes enables exponential speedups in fault-tolerant shadow tomography and cubic observable estimation over unencoded adaptive strategies.
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The Exact Replica Threshold for Nonlinear Moments of Quantum States
Exact replica threshold for tr(ρ^t) is ⌈t/2⌉, with fewer replicas incurring dimension-dependent sample complexity.