@inproceedings{1e7d678b887e44a9800bce21d1190792,

title = "The Quantum Complexity of Computing Schatten p-norms",

abstract = "We consider the quantum complexity of computing Schatten p-norms and related quantities, and 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. The same problem can be solved for arbitrary sparse matrices in BQP. One application of the algorithm is the approximate computation of the energy of a graph.",

keywords = "And phrases Schatten p-norm, Complexity theory, One clean qubit model, Quantum complexity theory",

author = "Chris Cade and Ashley Montanaro",

year = "2018",

month = jul,

doi = "10.4230/LIPIcs.TQC.2018.4",

language = "English",

series = "Leibniz International Proceedings in Informatics (LIPIcs)",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

pages = "4:1--4:20",

editor = "Stacey Jeffery",

booktitle = "13th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2018",

note = "13th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2018 ; Conference date: 16-07-2018 Through 18-07-2018",

}