Computational depth complexity of measurement-based quantum computation

  • Authors:

  • Dan Browne;Elham Kashefi;Simon Perdrix

  • Affiliations:

  • Department of Physics and Astronomy, University College London, UK;Laboratory for Foundations of Computer Science, University of Edinburgh, UK;CNRS, Laboratoire d'Informatique de Grenoble, Grenoble University, France

  • Venue:
  • TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

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.