Embedding experimental quantum states into high-distance codes enables exponential speedups in fault-tolerant shadow tomography and cubic observable estimation over unencoded adaptive strategies.
Theorem 12.LetN inj denote the sample complexity of the three-copy cycle test performed on injected copies ofρ subject to depolarizing noise of strengthλ′
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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.