Verification of concurrent quantum protocols by equivalence checking

Ardeshir-Larijani, Ebrahim, Gay, Simon J. and Nagarajan, Rajagopal ORCID: https://orcid.org/0000-0002-9724-4962 (2014) Verification of concurrent quantum protocols by equivalence checking. Tools and Algorithms for the Construction and Analysis of Systems: 20th International Conference, TACAS 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014, Grenoble, France, April 5-13, 2014. Proceedings. In: TACAS 2014: 20th International Conference on Tools and Algorithms for the Construction and Analysis of Systems,, 5-13 Apr 2014, Grenoble, France. ISBN 9783642548611, e-ISBN 9783642548628. ISSN 0302-9743 [Conference or Workshop Item] (doi:10.1007/978-3-642-54862-8_42)

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.

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