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Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis

文献类型：期刊论文

作者Sun, Xiaoming1,3; Tian, Guojing1,3; Yang, Shuai1,3; Yuan, Pei2; Zhang, Shengyu2
刊名IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
出版日期2023-10-01
卷号42期号:10页码:3301-3314
ISSN号0278-0070
关键词Circuit depth depth-space tradeoff quantum circuit state preparation unitary synthesis
DOI10.1109/TCAD.2023.3244885
英文摘要The quantum state preparation problem aims to prepare an n-qubit quantum state vertical bar psi(v)>> = Sigma(2n-1)(k=0)v(k)vertical bar k > from the initial state vertical bar 0(circle times n), for a given unit vector v = (v(0), v(1), v(2),..., v(2)(n-1))T is an element of C-2n with parallel to v parallel to(2) = 1. The problem is of fundamental importance in quantum algorithm design, Hamiltonian simulation and quantum machine learning, yet its circuit depth complexity remains open when ancillary qubits are available. In this article, we study quantum circuits when there are m ancillary qubits available. We construct, for any m, circuits that can prepare vertical bar v parallel to in depth O((2n/[m + n]) + n) and size O(2(n)), achieving the optimal value for both measures simultaneously. These results also imply a depth complexity of (4n/[m + n]) for quantum circuits implementing a general nqubit unitary for any m = O(2(n)/n) number of ancillary qubits. This resolves the depth complexity for circuits without ancillary qubits. And for circuits with exponentially many ancillary qubits, our result quadratically improves the currently best upper bound of O(4n) to (2n). Our circuits are deterministic, prepare the state and carry out the unitary precisely, utilize the ancillary qubits tightly and the depths are optimal in a wide parameter regime. The results can be viewed as (optimal) time-space tradeoff bounds, which is not only theoretically interesting, but also practically relevant in the current trend that the number of qubits starts to take off, by showing a way to use a large number of qubits to compensate the short qubit lifetime.
资助项目National Natural Science Foundation of China[61832003] ; Priority Research Program of Chinese Academy of Sciences[62272441] ; [XDB28000000]
WOS研究方向Computer Science ; Engineering
语种英语
出版者IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
WOS记录号WOS:001071466500011
源URL[http://119.78.100.204/handle/2XEOYT63/21129]  
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; Tian, Guojing; Yang, Shuai; Yuan, Pei; Zhang, Shengyu
作者单位1.Univ Chinese Acad Sci, Sch Comp Sci & Technol, Beijing 100049, Peoples R China
2.Tencent, Tencent Quantum Lab, Shenzhen 518057, Guangdong, Peoples R China
3.Chinese Acad Sci, Inst Comp Technol, State Key Lab Processors, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Sun, Xiaoming,Tian, Guojing,Yang, Shuai,et al. Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis[J]. IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS,2023,42(10):3301-3314.
APA Sun, Xiaoming,Tian, Guojing,Yang, Shuai,Yuan, Pei,&Zhang, Shengyu.(2023).Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis.IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS,42(10),3301-3314.
MLA Sun, Xiaoming,et al."Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis".IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 42.10(2023):3301-3314.

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来源：计算技术研究所

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