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DOI: 10.4230/LIPIcs.TQC.2015.191

Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices

Authors: Yoshifumi Nakata, Christoph Hirche, Ciara Morgan, and Andreas Winter

Published in: LIPIcs, Volume 44, 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)

Abstract

Unitary 2-designs are random unitary matrices which, in contrast to their Haar-distributed counterparts, have been shown to be efficiently realized by quantum circuits. Most notably, unitary 2-designs are known to achieve decoupling, a fundamental primitive of paramount importance in quantum Shannon theory. Here we prove that unitary 2-designs can be implemented approximately using random diagonal-unitaries.

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Yoshifumi Nakata, Christoph Hirche, Ciara Morgan, and Andreas Winter. Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 191-205, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{nakata_et_al:LIPIcs.TQC.2015.191,
  author =	{Nakata, Yoshifumi and Hirche, Christoph and Morgan, Ciara and Winter, Andreas},
  title =	{{Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices}},
  booktitle =	{10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)},
  pages =	{191--205},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-96-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{44},
  editor =	{Beigi, Salman and K\"{o}nig, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015.191},
  URN =		{urn:nbn:de:0030-drops-55570},
  doi =		{10.4230/LIPIcs.TQC.2015.191},
  annote =	{Keywords: unitary 2-designs, commuting quantum circuits}
}

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Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices

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