Quantum Circuit Design for Integer Multiplication Based on Schonhage-Strassen Algorithm

doi:10.1109/TCAD.2023.3279300

	Quantum Circuit Design for Integer Multiplication Based on Schonhage-Strassen Algorithm
	Nie, Junhong 1,2; Zhu, Qinlin 1,2; Li, Meng 1,2; Sun, Xiaoming 1,2,3
	2023-12-01
发表期刊	IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
ISSN	0278-0070
卷号	42 期号:12 页码:4791-4802
摘要	Quantum arithmetic circuits have attracted extensive attention recently since it plays fundamental roles in many applications of quantum computing. Specifically, quantum circuits for integer multiplication are of great significance to various quantum algorithms, including Shor's integer factorization and discrete logarithm algorithm. In this article, we design a family of quantum circuits for integer multiplication based on the famous classical integer multiplication algorithm, Schonhage-Strassen algorithm. We have made slight modifications to the algorithm to simplify its quantum circuit implementation. As a result, the quantum circuit we designed has gate depth O(log(2)n) . To the best of our knowledge, this is the first poly-logarithmic depth quantum circuit for integer multiplication which keeps the circuit size and the number of ancillary qubits subquadratic. Our design has size O(nlog nlog logn) counted by elementary quantum gates which is the same as the time complexity of the Schonhage-Strassen algorithm, and it consumes O(nlog nlog logn) clean ancillary qubits. In addition, we also utilize a weaker version of Schonhage-Strassen algorithm to give a family of circuits which has depth at the same order O(log(2)n) but with significantly smaller constants, while still keeping the size and number of ancillary qubits subquadratic.
关键词	Quantum circuit Qubit Arithmetic Logic gates Convolutional neural networks Time complexity Standards Integer programming Integer multiplication quantum circuit Sch\"onhage--Strassen algorithm
DOI	10.1109/TCAD.2023.3279300
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Hardware & Architecture ; Computer Science, Interdisciplinary Applications ; Engineering, Electrical & Electronic
WOS记录号	WOS:001123254100036
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计	被引频次：1[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/38851
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Sun, Xiaoming
作者单位	1.Chinese Acad Sci, Inst Comp Technol, State Key Lab Processors, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Comp Sci & Technol, Beijing 100049, Peoples R China 3.Shanghai Innovat Ctr Processor Technol, Shanghai 200234, Peoples R China
推荐引用方式 GB/T 7714	Nie, Junhong,Zhu, Qinlin,Li, Meng,et al. Quantum Circuit Design for Integer Multiplication Based on Schonhage-Strassen Algorithm[J]. IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS,2023,42(12):4791-4802.
APA	Nie, Junhong,Zhu, Qinlin,Li, Meng,&Sun, Xiaoming.(2023).Quantum Circuit Design for Integer Multiplication Based on Schonhage-Strassen Algorithm.IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS,42(12),4791-4802.
MLA	Nie, Junhong,et al."Quantum Circuit Design for Integer Multiplication Based on Schonhage-Strassen Algorithm".IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 42.12(2023):4791-4802.