Computational Depth Complexity of Measurement-Based Quantum Computation

  • Dan Browne
  • Elham Kashefi
  • Simon Perdrix
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6519)


In this paper, we mainly prove that the “depth of computations” in the one-way model is equivalent, up to a classical side-processing of logarithmic depth, to the quantum circuit model augmented with unbounded fanout gates. It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a very powerful model of quantum computation. It confirms and completes previous results which have pointed out, for some specific problems, a depth separation between the one-way model and the quantum circuit model. Since one-way model has the same parallel power as unbounded quantum fan-out circuits, the quantum Fourier transform can be approximated in constant depth in the one-way model, and thus the factorisation can be done by a polytime probabilistic classical algorithm which has access to a constant-depth one-way quantum computer. The extra power of the one-way model, comparing with the quantum circuit model, comes from its classical-quantum hybrid nature. We show that this extra power is reduced to the capability to perform unbounded classical parity gates in constant depth.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dan Browne
    • 1
  • Elham Kashefi
    • 2
  • Simon Perdrix
    • 3
  1. 1.Department of Physics and AstronomyUniversity College LondonUK
  2. 2.Laboratory for Foundations of Computer ScienceUniversity of EdinburghUK
  3. 3.CNRS, Laboratoire d’Informatique de GrenobleGrenoble UniversityFrance

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