The Quantum Complexity of Computing Schatten p-norms

Chris Cade, Ashley Montanaro

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

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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.

Original languageEnglish
Title of host publication13th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2018
EditorsStacey Jeffery
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages4:1-4:20
Number of pages20
ISBN (Electronic)9783959770804
DOIs
Publication statusPublished - Jul 2018
Event13th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2018 - Sydney, Australia
Duration: 16 Jul 201818 Jul 2018

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
Volume111
ISSN (Print)1868-8969

Conference

Conference13th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2018
CountryAustralia
CitySydney
Period16/07/1818/07/18

Keywords

  • And phrases Schatten p-norm
  • Complexity theory
  • One clean qubit model
  • Quantum complexity theory

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