On the Formal Verification of Optical Quantum Gates in HOL

  • Mohamed Yousri Mahmoud
  • Prakash Panangaden
  • Sofiène Tahar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9128)

Abstract

Quantum computers are expected to handle hard computational problems and provide unbreakable security protocols. Among different quantum computer implementations, those based on quantum optics and nuclear magnetic resonance show good advancement in building large scale machines. However, the involvement of optical and nuclear techniques makes their development very critical. This motivates us to apply formal techniques, in particular theorem proving, in quantum circuits analysis. In this work, we present the formalization of multi-inputs/multi-outputs quantum gates (technically called multi-modes optical circuits). This requires the implementation of tensor product over complex-valued functions. Firstly, we build a formal model of single optical beams and then extend it to cover circuits of multi optical beams, with the help of the developed tensor product algebra. As an application, we formally verify the behavior of the optical quantum CNOT gate and Mach-Zehnder interferometer.

Keywords

Quantum computing Multi-modes Tensor product CNOT gate Mach-Zehnder Theorm proving HOL light 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mohamed Yousri Mahmoud
    • 1
  • Prakash Panangaden
    • 2
  • Sofiène Tahar
    • 1
  1. 1.Electrical and Computer Engineering DeptartmentConcordia UniversityMontrealCanada
  2. 2.Computer Science DepartmentMcgill UniversityMontrealCanada

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