Quantum-classical algorithms for skewed linear systems with an optimized Hadamard test

doi:10.1103/PhysRevA.103.042422

	Quantum-classical algorithms for skewed linear systems with an optimized Hadamard test
	Wu, Bujiao 2,3; Ray, Maharshi 1; Zhao, Liming 1; Sun, Xiaoming 2,3; Rebentrost, Patrick 1
刊名	PHYSICAL REVIEW A
	2021-04-23
卷号	103 期号:4 页码:18
ISSN号	2469-9926
DOI	10.1103/PhysRevA.103.042422
英文摘要	The solving of linear systems provides a rich area to investigate the use of nearer-term, noisy, intermediate-scale quantum computers. In this work, we discuss hybrid quantum-classical algorithms for heavily skewed linear systems for overdetermined and underdetermined cases. Our input model is such that the columns or rows of the matrix defining the linear system are given via quantum circuits of polylogarithmic depth and the number of circuits is much smaller than their Hilbert space dimension. Our algorithms have polylogarithmic dependence on the dimension and polynomial dependence in other natural quantities. In addition, we present an algorithm for the special case of a factorized linear system with run time polylogarithmic in the respective dimensions. At the core of these algorithms is the Hadamard test and in the second part of this paper, we consider the optimization of the circuit depth of this test. Given an n-qubit and d-depth quantum circuit C, we can approximate < 0 vertical bar C vertical bar 0 > using (n + s) qubits and O(log(2) s + d log(2) (n/s) + d)-depth quantum circuits, where s <= n. In comparison, the standard implementation requires n + 1 qubits and O(dn) depth. Lattice geometries underlie recent quantum supremacy experiments with superconducting devices. We also optimize the Hadamard test for an (l(1) x l(2)) lattice with l(1) x l(2) = n and can approximate < 0 vertical bar C vertical bar 0 > with (n + 1) qubits and O(d(l(1) + l(2)))-depth circuits. In comparison, the standard depth is O(dn(2)) in this setting. Both of our optimization methods are asymptotically tight in the case of one-depth quantum circuits C.
资助项目	Singapore National Research Foundation ; Prime Minister's Office, Singapore ; Ministry of Education, Singapore under the Research Centres of Excellence programme[R 710-000-012-135] ; National Natural Science Foundation of China[61832003] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDB28000000] ; K.C. Wong Education Foundation
WOS研究方向	Optics ; Physics
语种	英语
出版者	AMER PHYSICAL SOC
WOS记录号	WOS:000646161200003
内容类型	期刊论文
源URL	[http://119.78.100.204/handle/2XEOYT63/17754]
专题	中国科学院计算技术研究所
通讯作者	Wu, Bujiao; Rebentrost, Patrick
作者单位	1.Natl Univ Singapore, Ctr Quantum Technol, Singapore 117543, Singapore 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wu, Bujiao,Ray, Maharshi,Zhao, Liming,et al. Quantum-classical algorithms for skewed linear systems with an optimized Hadamard test[J]. PHYSICAL REVIEW A,2021,103(4):18.
APA	Wu, Bujiao,Ray, Maharshi,Zhao, Liming,Sun, Xiaoming,&Rebentrost, Patrick.(2021).Quantum-classical algorithms for skewed linear systems with an optimized Hadamard test.PHYSICAL REVIEW A,103(4),18.
MLA	Wu, Bujiao,et al."Quantum-classical algorithms for skewed linear systems with an optimized Hadamard test".PHYSICAL REVIEW A 103.4(2021):18.