Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices

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



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Yoshifumi Nakata
Christoph Hirche
Ciara Morgan
Andreas Winter

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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)
https://doi.org/10.4230/LIPIcs.TQC.2015.191

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.
Keywords
  • unitary 2-designs
  • commuting quantum circuits

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