Quadratic Form Expansions for Unitaries

  • Niel de Beaudrap
  • Vincent Danos
  • Elham Kashefi
  • Martin Roetteler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5106)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Niel de Beaudrap
    • 1
  • Vincent Danos
    • 2
  • Elham Kashefi
    • 3
  • Martin Roetteler
    • 4
  1. 1.IQC, University of WaterlooCanada
  2. 2.School of InformaticsUniversity of EdinburghUK
  3. 3.Laboratoire d’Informatique de GrenobleFrance
  4. 4.NEC Laboratories America, Inc.USA

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