## Abstract

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 language | English |
---|---|

Article number | 8543237 |

Pages (from-to) | 729-739 |

Number of pages | 11 |

Journal | IEEE Transactions on Computers |

Volume | 68 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2019 |

## Keywords

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

## ASJC Scopus subject areas

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