Automatic synthesis of quaternary quantum circuits

Mozammel H.A. Khan, Himanshu Thapliyal, Edgard Munoz-Coreas

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish
Pages (from-to)1733-1759
Number of pages27
JournalJournal of Supercomputing
Issue number5
StatePublished - May 1 2017

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.


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

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Information Systems
  • Hardware and Architecture


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