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The Journal of Supercomputing

, Volume 73, Issue 5, pp 1733–1759 | Cite as

Automatic synthesis of quaternary quantum circuits

  • Mozammel H. A. Khan
  • Himanshu Thapliyal
  • Edgard Munoz-Coreas
Article

Abstract

Quaternary encoded binary circuits are more compact than their binary counterpart. Although quaternary reversible circuits are realizable, design of such circuits is still in its infancy. This work proposes a new, enhanced method of quaternary Galois field sum of products (QGFSOP) synthesis for quaternary quantum circuits. To reduce QGFSOP product terms, the algorithm makes use of 11 newly defined quaternary Galois field (QGF) expansions (for a total of 21 QGF expansions). This algorithm achieves QGFSOP minimization with the assistance of a pseudo-Kronecker Galois field decision diagram (QGFDD). This is a novel approach for QGFSOP synthesis. Finally, QGFSOP expressions are translated into quantum cost optimized quaternary quantum circuits using: (1) newly developed quaternary quantum gate realizations of controlled Feynman and Toffoli gate that are optimized in terms of quantum cost, (2) use of composite literals consisting of 1 digit and M–S gates. Performance evaluation against existing works in the literature determined that our proposed method achieves an average QGFSOP expression product term savings of 32.66 %. Also, the synthesized QGFSOP circuits were evaluated in terms of quantum cost.

Keywords

Quaternary Galois field decision diagram Quaternary Galois field sum of products minimization Quaternary reversible circuit design 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Mozammel H. A. Khan
    • 1
  • Himanshu Thapliyal
    • 2
  • Edgard Munoz-Coreas
    • 2
  1. 1.Department of Computer Science and EngineeringEast West UniversityDhakaBangladesh
  2. 2.Department of Electrical and Computer EngineeringUniversity of KentuckyLexingtonUSA

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