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2 results

  • 4 - Averaging

  • Chris Godsil, University of Waterloo, Ontario, Hanmeng Zhan, Simon Fraser University, British Columbia
  • Book:
    Discrete Quantum Walks on Graphs and Digraphs
    Published online:
    23 December 2022
    Print publication:
    12 January 2023, pp 41-58

  • Summary

    The axioms of quantum physics imply that in general it makes no sense to speak of the long-term behaviour of a quantum walk. In this chapter we introduce a process that allows us to develop a meaningful substitute for a simple average.

  • 7 - Shunts

  • Chris Godsil, University of Waterloo, Ontario, Hanmeng Zhan, Simon Fraser University, British Columbia
  • Book:
    Discrete Quantum Walks on Graphs and Digraphs
    Published online:
    23 December 2022
    Print publication:
    12 January 2023, pp 98-120

  • Summary

    Aharonov et al. introduced class of quantum walks where the transition matrix is not (in general) a product of two reflections. (We call these shunt-decomposition walks.) In consequence, analysis of these walks is more difficult than the walks met with in earlier chapters. However the state space of walks is still the space of complex functions on the arcs of a graph. We give a description of these walks in graph theoretic terms, and study their behaviour.