Designs of the divider and special multiplier optimizing T and CNOT gates

IF 5.8 2区 物理与天体物理 Q1 OPTICS
Ping Fan, Hai-Sheng Li
{"title":"Designs of the divider and special multiplier optimizing T and CNOT gates","authors":"Ping Fan,&nbsp;Hai-Sheng Li","doi":"10.1140/epjqt/s40507-024-00222-4","DOIUrl":null,"url":null,"abstract":"<div><p>Quantum circuits for multiplication and division are necessary for scientific computing on quantum computers. Clifford + T circuits are widely used in fault-tolerant realizations. T gates are more expensive than other gates in Clifford + T circuits. But neglecting the cost of CNOT gates may lead to a significant underestimation. Moreover, the small number of qubits available in existing quantum devices is another constraint on quantum circuits. As a result, reducing T-count, T-depth, CNOT-count, CNOT-depth, and circuit width has become the important optimization goal. We use 3-bit Hermitian gates to design basic arithmetic operations. Then, we present a special multiplier and a divider using basic arithmetic operations, where ‘special’ means that one of the two operands of multiplication is non-zero. Next, we use new rules to optimize the Clifford + T circuits of the special multiplier and divider in terms of T-count, T-depth, CNOT-count, CNOT-depth, and circuit width. Comparative analysis shows that the proposed multiplier and divider have lower T-count, T-depth, CNOT-count, and CNOT-depth than the current works. For instance, the proposed 32-bit divider achieves improvement ratios of 40.41 percent, 31.64 percent, 45.27 percent, and 65.93 percent in terms of T-count, T-depth, CNOT-count, and CNOT-depth compared to the best current work. Further, the circuit widths of the proposed <i>n</i>-bit multiplier and divider are 3<i>n</i>. I.e., our multiplier and divider reach the minimum width of multipliers and dividers, keeping an operand unchanged.</p></div>","PeriodicalId":547,"journal":{"name":"EPJ Quantum Technology","volume":null,"pages":null},"PeriodicalIF":5.8000,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-024-00222-4","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPJ Quantum Technology","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1140/epjqt/s40507-024-00222-4","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0

Abstract

Quantum circuits for multiplication and division are necessary for scientific computing on quantum computers. Clifford + T circuits are widely used in fault-tolerant realizations. T gates are more expensive than other gates in Clifford + T circuits. But neglecting the cost of CNOT gates may lead to a significant underestimation. Moreover, the small number of qubits available in existing quantum devices is another constraint on quantum circuits. As a result, reducing T-count, T-depth, CNOT-count, CNOT-depth, and circuit width has become the important optimization goal. We use 3-bit Hermitian gates to design basic arithmetic operations. Then, we present a special multiplier and a divider using basic arithmetic operations, where ‘special’ means that one of the two operands of multiplication is non-zero. Next, we use new rules to optimize the Clifford + T circuits of the special multiplier and divider in terms of T-count, T-depth, CNOT-count, CNOT-depth, and circuit width. Comparative analysis shows that the proposed multiplier and divider have lower T-count, T-depth, CNOT-count, and CNOT-depth than the current works. For instance, the proposed 32-bit divider achieves improvement ratios of 40.41 percent, 31.64 percent, 45.27 percent, and 65.93 percent in terms of T-count, T-depth, CNOT-count, and CNOT-depth compared to the best current work. Further, the circuit widths of the proposed n-bit multiplier and divider are 3n. I.e., our multiplier and divider reach the minimum width of multipliers and dividers, keeping an operand unchanged.

优化 T 门和 CNOT 门的除法器和特殊乘法器设计
在量子计算机上进行科学计算需要乘除量子电路。克利福德 + T 电路广泛用于容错实现。在 Clifford + T 电路中,T 门比其他门更昂贵。但忽略 CNOT 门的成本可能会导致严重低估。此外,现有量子设备的量子比特数量较少,这也是量子电路的另一个限制因素。因此,减少 T 数、T 深度、CNOT 数、CNOT 深度和电路宽度成为重要的优化目标。我们使用 3 位 Hermitian 门来设计基本算术运算。然后,我们利用基本算术运算提出了一个特殊的乘法器和一个除法器,其中 "特殊 "是指乘法的两个操作数之一为非零。接下来,我们使用新规则,从 T 数、T 深度、CNOT 数、CNOT 深度和电路宽度等方面优化了特殊乘法器和除法器的 Clifford + T 电路。对比分析表明,与现有的乘法器和除法器相比,建议的乘法器和除法器具有更低的 T-count、T-depth、CNOT-count 和 CNOT-depth。例如,与目前最好的作品相比,拟议的 32 位除法器在 T-count、T-depth、CNOT-count 和 CNOT-depth 方面分别实现了 40.41%、31.64%、45.27% 和 65.93% 的改进率。此外,建议的 n 位乘法器和除法器的电路宽度为 3n。也就是说,在操作数不变的情况下,我们的乘法器和除法器达到了乘法器和除法器的最小宽度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
EPJ Quantum Technology
EPJ Quantum Technology Physics and Astronomy-Atomic and Molecular Physics, and Optics
CiteScore
7.70
自引率
7.50%
发文量
28
审稿时长
71 days
期刊介绍: Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following: Quantum measurement, metrology and lithography Quantum complex systems, networks and cellular automata Quantum electromechanical systems Quantum optomechanical systems Quantum machines, engineering and nanorobotics Quantum control theory Quantum information, communication and computation Quantum thermodynamics Quantum metamaterials The effect of Casimir forces on micro- and nano-electromechanical systems Quantum biology Quantum sensing Hybrid quantum systems Quantum simulations.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信