Quantum circuit design of a T-count optimized integer multiplier

Edgard Munoz-Coreas, Himanshu Thapliyal

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


Quantum circuits of many qubits are extremely difficult to realize; thus, the number of qubits is an important metric in a quantum circuit design. Further, scalable and reliable quantum circuits are based on fault tolerant implementations of quantum gates such as Clifford+T gates. An efficient quantum circuit saves quantum hardware resources by reducing the number of T gates without substantially increasing the number of qubits. This work presents a T-count optimized quantum circuit for integer multiplication with only 4 ⊙ n + 14·n+1 qubits and no garbage outputs. The proposed quantum multiplier design reduces the T-count by using a novel quantum conditional adder circuit. Also, where one operand to the conditional adder is zero, the conditional adder is replaced with a Toffoli gate array to further save T gates. Average T-count savings of 46.12, 47.55, 62.71 and 26.30 percent are achieved compared to the recent works by Kotiyal et al., Babu, Lin et al., and Jayashree et al., respectively.

Original languageEnglish
Article number8543237
Pages (from-to)729-739
Number of pages11
JournalIEEE Transactions on Computers
Issue number5
StatePublished - May 1 2019

Bibliographical note

Publisher Copyright:
© 1968-2012 IEEE.


  • Quantum computing
  • clifford+T gates
  • conditional adder
  • integer multiplication
  • quantum arithmetic
  • quantum circuits

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics


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