The circuit design and optimization of quantum multiplier and divider  

作　　者：Hai-Sheng Li Ping Fan Haiying Xia Gui-Lu Long 

机构地区：[1]College of Electronic Engineering,Guangxi Normal University,Guilin 541004,China [2]College of Information Engineering,East China JiaoTong University,Nanchang 330013,China [3]Department of Physics,Tsinghua University,Beijing 100084,China [4]State Key Laboratory of Low-Dimensional Quantum Physics,Tsinghua University,Beijing 100084,China [5]Beijing National Research Center for Information Science and Technology,Beijing 100084,China [6]Beijing Academy of Quantum Information Sciences,Beijing 100193,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2022年第6期11-25,共15页中国科学：物理学、力学、天文学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.61762012,61763014,and 62062035);the Science and Technology Project of Guangxi(Grant No.2020GXNSFDA238023).

摘　　要：A fault-tolerant circuit is required for robust quantum computing in the presence of noise.Clifford+T circuits are widely used in fault-tolerant implementations.As a result,reducing T-depth,T-count,and circuit width has emerged as important optimization goals.A measure-and-fixup approach yields the best T-count for arithmetic operations,but it requires quantum measurements.This paper proposes approximate Toffoli,TR,Peres,and Fredkin gates with optimized T-depth and T-count.Following that,we implement basic arithmetic operations such as quantum modular adder and subtractor using approximate gates that do not require quantum measurements.Then,taking into account the circuit width,T-depth,and T-count,we design and optimize the circuits of two multipliers and a divider.According to the comparative analysis,the proposed multiplier and divider circuits have lower circuit width,T-depth,and T-count than the current works that do not use the measure-and-fixup approach.Significantly,the proposed second multiplier produces approximately 77%T-depth,60%T-count,and 25%width reductions when compared to the existing multipliers without quantum measurements.

关 键 词：quantum multiplier quantum divider quantum fault-tolerant circuit quantum computing 

分 类 号：O413[理学—理论物理] TN791[理学—物理]