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Quadratic Form Expansions for Unitaries

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http://dx.doi.org/10.1007/978-3-540-89304-2_4
Original languageEnglish
Title of host publicationTheory of Quantum Computation, Communication, and Cryptography
Subtitle of host publicationThird Workshop, TQC 2008 Tokyo, Japan, January 30 - February 1, 2008. Revised Selected Papers
EditorsYasuhito Kawano, Michele Mosca
PublisherSpringer Berlin Heidelberg
Pages29-46
Number of pages18
Volume5106
ISBN (Electronic)978-3-540-89304-2
ISBN (Print)978-3-540-89303-5
DOIs
Publication statusPublished - 2008

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
Volume5106

Abstract

We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis where the phase contributed by each path is described by a quadratic form over ℝ. We show how to relate such a form to an entangled resource akin to that of the one-way measurement model of quantum computing. Using this, we describe various conditions under which it is possible to efficiently implement a unitary operation U, either when provided a quadratic form expansion for U as input, or by finding a quadratic form expansion for U from other input data.

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