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.


Unitary Transformation Quantum Circuit Pauli Operator Entanglement Graph Fractional Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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