Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-20T11:32:27.374Z Has data issue: false hasContentIssue false
  • English
  • Français

Extended phase map decompositions for unitaries

Published online by Cambridge University Press:  28 February 2013

VEDRAN DUNJKO  and
ELHAM KASHEFI
VEDRAN DUNJKO
Affiliation:
Department of Physics, Heriot-Watt University, Edinburgh, United Kingdom, and School of Informatics, University of Edinburgh, Edinburgh, United Kingdom Email: [email protected]
ELHAM KASHEFI
Affiliation:
School of Informatics, University of Edinburgh, Edinburgh, United Kingdom Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a complete structural characterisation of the map implemented by the positive branch of a one-way pattern. Our approach is based on the phase map decomposition (de Beaudrap et al. 2006; de Beaudrap et al. 2008) and leads to some preliminary results on the connection between the column structure of a given unitary and the angles of measurements in a pattern that implements it. Our characterisation highlights the role of entanglement in the efficiency of the simulation of a one-way pattern, and it is a step forward towards a full characterisation of those unitaries that have an efficient one-way model implementation.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Special Issue 2: Developments In Computational Models 2010 , April 2013 , pp. 360 - 385
Copyright
Copyright © Cambridge University Press 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

de Beaudrap, N., Danos, V. and Kashefi, E. (2006) Phase map decomposition for unitaries. Available at quant-ph/0603266.Google Scholar
de Beaudrap, N., Danos, V., Kashefi, E. and Roetteler, M. (2008) Quadratic form expansions for unitaries. In: Kawano, Y. and Mosca, M. (eds.) Theory of Quantum Computation, Communication, and Cryptography Third Workshop, TQC 2008. Springer-Verlag Lecture Notes in Computer Science 5106 29–46.CrossRefGoogle Scholar
Browne, D., Kashefi, E., Mhalla, M. and Perdrix, S. (2007) Generalized flow and determinism in measurement-based quantum computation. New Journal of Physics 9.CrossRefGoogle Scholar
Danos, V. and Kashefi, E. (2006) Determinism in the one-way model. Physical Review A 74 (5)052310.CrossRefGoogle Scholar
Danos, V., Kashefi, E. and Panangaden, P. (2007) The measurement calculus. Journal of ACM 54 (2)8.CrossRefGoogle Scholar
Danos, V., Kashefi, E., Panangaden, P. and Perdrix, S. (2009) Extended measurement calculus. In: Gay, S. and Mackie, I. (eds.) Semantic Techniques in Quantum Computation, Cambridge University Press.Google Scholar
Kashefi, E., Markham, D., Mhalla, M. and Perdrix, S. (2009) Information flow in secret sharing protocols. Electronic Proceedings in Theoretical Computer Science 9 87–97.CrossRefGoogle Scholar
Raussendorf, R. and Briegel, H. J. (2001) A one-way quantum computer. Physical Review Letters 86 (5188).CrossRefGoogle ScholarPubMed
Raussendorf, R., Browne, D. E. and Briegel, H. J. (2003) Measurement-based quantum computation with cluster states. Physical Review A 68 022312.CrossRefGoogle Scholar