T-count and qubit optimized quantum circuit design of the non-restoring square root algorithm

Edgard Muñoz-Coreas, Himanshu Thapliyal

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant, but the T gate is very costly to implement. As a result, reducing T-count has become an important optimization goal. Further, quantum circuits with many qubits are difficult to realize, making designs that save qubits and produce no garbage outputs desirable. In this work, we present a T-count optimized quantum square root circuit with only 2 · n + 1 qubits and no garbage output. To make a fair comparison against existing work, the Bennett’s garbage removal scheme is used to remove garbage output from existing works. We determined that out proposed design achieves an average T-count savings of 43.44%, 98.95%, 41.06%, and 20.28% as well as qubit savings of 85.46%, 95.16%, 90.59%, and 86.77% compared to existing works.

Original languageEnglish
Article number37
JournalACM Journal on Emerging Technologies in Computing Systems
Issue number3
StatePublished - Oct 2018

Bibliographical note

Publisher Copyright:
© 2018 Association for Computing Machinery.


  • Non-restoring division
  • Quantum arithmetic circuit
  • Quantum gate
  • Resource optimization

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Electrical and Electronic Engineering


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