Mapping of subtractor and adder-subtractor circuits on reversible quantum gates

Himanshu Thapliyal

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

36 Scopus citations


Reversible arithmetic units such as adders, subtractors and comparators form the essential components of any hardware implementation of quantum algorithms such as Shor’s factoring algorithm. Further, the synthesis methods proposed in the existing literature for reversible circuits target combinational and sequential circuits in general and are not suitable for synthesis of reversible arithmetic units. In this paper, we present several design methodologies for reversible subtractor and reversible adder-subtractor circuits, and a framework for synthesizing reversible arithmetic circuits. Three different design methodologies are proposed for the design of reversible ripple borrow subtractor that vary in terms of optimization of metrics such as ancilla inputs, garbage outputs, quantum cost and delay. The first approach follows the traditional ripple carry approach while the other two use the properties that the subtraction operation can be defined as (Formula presented.), respectively. Next, we derive methodologies adapting the subtractor to also perform addition as selected with a control signal. Finally, a new synthesis framework for automatic generation of reversible arithmetic circuits optimizing the metrics of ancilla inputs, garbage outputs, quantum cost and the delay is presented that integrates the various methodologies described in our work.

Original languageEnglish
Title of host publicationTransactions on Computational Science XXVII
EditorsMarina L. Gavrilova, C.J. Kenneth Tan
Number of pages25
StatePublished - 2016
EventTransactions on Computational Science XXVII - San Diego, United States
Duration: Jan 1 2016 → …

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceTransactions on Computational Science XXVII
Country/TerritoryUnited States
CitySan Diego
Period1/1/16 → …

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2016.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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