LIPIcs.TQC.2015.191.pdf
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Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices
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10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2015-11-04
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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.
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Keywords
- unitary 2-designs
- commuting quantum circuits
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