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The Quantum Complexity of Computing Schatten p-norms

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In this talk I will present some results on the quantum complexity of computing Schatten p-norms and related quantities. We find that the problem of estimating these quantities is closely related to the one clean qubit model of computation. We show that the problem of approximating Tr(|A|^p) for a log-local n-qubit Hamiltonian A and p=poly(n), up to a suitable level of accuracy, is contained in DQC1 ; and that approximating this quantity up to a somewhat higher level of accuracy is DQC1 -hard. In some cases the level of accuracy achieved by the quantum algorithm is substantially better than a natural classical algorithm for the problem.

This talk is part of the CQIF Seminar series.

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