Embedding experimental quantum states into high-distance codes enables exponential speedups in fault-tolerant shadow tomography and cubic observable estimation over unencoded adaptive strategies.
Here we demonstrate that such a lower bound can also be established for more general observable-estimation tasks of the formtr Oρ3
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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.