Quadratic Form Expansions for Unitaries

Niel de Beaudrap; Vincent Danos; Elham Kashefi; Martin Roetteler

doi:10.1007/978-3-540-89304-2_4

Quadratic Form Expansions for Unitaries

Niel de Beaudrap, Vincent Danos, Elham Kashefi, Martin Roetteler

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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.

Original language	English
Title of host publication	Theory of Quantum Computation, Communication, and Cryptography
Subtitle of host publication	Third Workshop, TQC 2008 Tokyo, Japan, January 30 - February 1, 2008. Revised Selected Papers
Editors	Yasuhito Kawano, Michele Mosca
Publisher	Springer Berlin Heidelberg
Pages	29-46
Number of pages	18
Volume	5106
ISBN (Electronic)	978-3-540-89304-2
ISBN (Print)	978-3-540-89303-5
DOIs	https://doi.org/10.1007/978-3-540-89304-2_4
Publication status	Published - 2008

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer Berlin Heidelberg
Volume	5106

Access to Document

10.1007/978-3-540-89304-2_4

de Beaudrap Danos ET AL 2008 Quafratic Form Expansions for UnitariesAccepted author manuscript, 246 KB

http://dx.doi.org/10.1007/978-3-540-89304-2_4

Measurement based quantum computing and it's relation to other quantum models
Kashefi, E.
EPSRC
1/03/08 → 31/07/13
Project: Research

Cite this

de Beaudrap, N., Danos, V., Kashefi, E., & Roetteler, M. (2008). Quadratic Form Expansions for Unitaries. In Y. Kawano, & M. Mosca (Eds.), Theory of Quantum Computation, Communication, and Cryptography: Third Workshop, TQC 2008 Tokyo, Japan, January 30 - February 1, 2008. Revised Selected Papers (Vol. 5106, pp. 29-46). (Lecture Notes in Computer Science; Vol. 5106). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-89304-2_4

de Beaudrap, Niel ; Danos, Vincent ; Kashefi, Elham et al. / Quadratic Form Expansions for Unitaries. Theory of Quantum Computation, Communication, and Cryptography: Third Workshop, TQC 2008 Tokyo, Japan, January 30 - February 1, 2008. Revised Selected Papers. editor / Yasuhito Kawano ; Michele Mosca. Vol. 5106 Springer Berlin Heidelberg, 2008. pp. 29-46 (Lecture Notes in Computer Science).

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title = "Quadratic Form Expansions for Unitaries",

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de Beaudrap, N, Danos, V , Kashefi, E & Roetteler, M 2008, Quadratic Form Expansions for Unitaries. in Y Kawano & M Mosca (eds), Theory of Quantum Computation, Communication, and Cryptography: Third Workshop, TQC 2008 Tokyo, Japan, January 30 - February 1, 2008. Revised Selected Papers. vol. 5106, Lecture Notes in Computer Science, vol. 5106, Springer Berlin Heidelberg, pp. 29-46. https://doi.org/10.1007/978-3-540-89304-2_4

Quadratic Form Expansions for Unitaries. / de Beaudrap, Niel; Danos, Vincent ; Kashefi, Elham et al.

Theory of Quantum Computation, Communication, and Cryptography: Third Workshop, TQC 2008 Tokyo, Japan, January 30 - February 1, 2008. Revised Selected Papers. ed. / Yasuhito Kawano; Michele Mosca. Vol. 5106 Springer Berlin Heidelberg, 2008. p. 29-46 (Lecture Notes in Computer Science; Vol. 5106).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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T1 - Quadratic Form Expansions for Unitaries

AU - de Beaudrap, Niel

AU - Danos, Vincent

AU - Kashefi, Elham

AU - Roetteler, Martin

PY - 2008

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N2 - 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.

AB - 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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DO - 10.1007/978-3-540-89304-2_4

M3 - Conference contribution

SN - 978-3-540-89303-5

VL - 5106

T3 - Lecture Notes in Computer Science

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BT - Theory of Quantum Computation, Communication, and Cryptography

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de Beaudrap N, Danos V , Kashefi E, Roetteler M. Quadratic Form Expansions for Unitaries. In Kawano Y, Mosca M, editors, Theory of Quantum Computation, Communication, and Cryptography: Third Workshop, TQC 2008 Tokyo, Japan, January 30 - February 1, 2008. Revised Selected Papers. Vol. 5106. Springer Berlin Heidelberg. 2008. p. 29-46. (Lecture Notes in Computer Science). doi: 10.1007/978-3-540-89304-2_4

Quadratic Form Expansions for Unitaries

Abstract

Publication series

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Projects

Measurement based quantum computing and it's relation to other quantum models

Cite this