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

doi:10.1109/TCAD.2023.3244885

	Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis
	Sun, Xiaoming 1,2; Tian, Guojing 1,2; Yang, Shuai 1,2; Yuan, Pei 3; Zhang, Shengyu 3
	2023-10-01
发表期刊	IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
ISSN	0278-0070
卷号	42 期号:10 页码:3301-3314
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.
关键词	Circuit depth depth-space tradeoff quantum circuit state preparation unitary synthesis
DOI	10.1109/TCAD.2023.3244885
收录类别	SCI
语种	英语
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
WOS类目	Computer Science, Hardware & Architecture ; Computer Science, Interdisciplinary Applications ; Engineering, Electrical & Electronic
WOS记录号	WOS:001071466500011
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计	被引频次：17[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/2XEOYT63/21130
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.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.Tencent, Tencent Quantum Lab, Shenzhen 518057, Guangdong, 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.