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A modeling and verification framework for optical quantum circuits

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Formal Aspects of Computing

Abstract

Quantum computing systems promise to increase the capabilities for solving problems which classical computers cannot handle adequately, such as integers factorization. In this paper, we present a formal modeling and verification approach for optical quantum circuits, where we build a rich library of optical quantum gates and develop a proof strategy in higher-order logic to reason about optical quantum circuits automatically. The constructed library contains a variety of quantum gates ranging from 1-qubit to 3-qubit gates that are sufficient to model most existing quantum circuits. As real world applications, we present the formal analysis of several quantum circuits including quantum full adders and the Grover’s oracle circuits, for which we have proved the behavioral correctness and calculated the operational success rate, which has never been provided in the literature. We show through several case studies the efficiency of the proposed framework in terms of the scalability and modularity.

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Acknowledgements

This work has been supported in part by the Canadian federal research funding agency NSERC, Grant No. RGPIN/06809-2015. We wish also to thank the Associate Editor and the Anonymous Referees for their comments which helped to improve the paper.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada

    Sidi Mohamed Beillahi & Sofiène Tahar

  2. Department of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Mohamed Yousri Mahmoud

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  1. Sidi Mohamed Beillahi
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  2. Mohamed Yousri Mahmoud
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  3. Sofiène Tahar
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Correspondence to Sofiène Tahar.

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Beillahi, S.M., Mahmoud, M.Y. & Tahar, S. A modeling and verification framework for optical quantum circuits. Form Asp Comp 31, 321–351 (2019). https://doi.org/10.1007/s00165-019-00480-5

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