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Verification of Concurrent Quantum Protocols by Equivalence Checking

  • Ebrahim Ardeshir-Larijani
  • Simon J. Gay
  • Rajagopal Nagarajan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8413)

Abstract

We present a tool which uses a concurrent language for describing quantum systems, and performs verification by checking equivalence between specification and implementation. In general, simulation of quantum systems using current computing technology is infeasible. We restrict ourselves to the stabilizer formalism, in which there are efficient simulation algorithms. In particular, we consider concurrent quantum protocols that behave functionally in the sense of computing a deterministic input-output relation for all interleavings of the concurrent system. Crucially, these input-output relations can be abstracted by superoperators, enabling us to take advantage of linearity. This allows us to analyse the behaviour of protocols with arbitrary input, by simulating their operation on a finite basis set consisting of stabilizer states. Despite the limitations of the stabilizer formalism and also the range of protocols that can be analysed using this approach, we have applied our equivalence checking tool to specify and verify interesting and practical quantum protocols from teleportation to secret sharing.

Keywords

Quantum State Model Check Density Operator Secret Sharing Equivalence Check 
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 2014

Authors and Affiliations

  • Ebrahim Ardeshir-Larijani
    • 1
    • 2
  • Simon J. Gay
    • 2
  • Rajagopal Nagarajan
    • 3
  1. 1.Department of Computer ScienceUniversity of WarwickUK
  2. 2.School of Computing ScienceUniversity of GlasgowUK
  3. 3.Department of Computer Science, School of Science and TechnologyMiddlesex UniversityUK

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