Shadow tomography of quantum states with prediction

doi:10.1007/s11704-024-40414-w

	Shadow tomography of quantum states with prediction
	Jiang, Jiyu 1; Wan, Zongqi 2,3; Li, Tongyang 4,5; Shao, Meiyue 1,6; Zhang, Jialin 2,3
	2025-07-01
发表期刊	FRONTIERS OF COMPUTER SCIENCE
ISSN	2095-2228
卷号	19 期号:7 页码:12
摘要	The shadow tomography problem introduced by [1] is an important problem in quantum computing. Given an unknown n-qubit quantum state rho, the goal is to estimate tr(F1 rho),& mldr;,(FM rho) using as least copies of rho as possible, within an additive error of epsilon, where F1,& mldr;,FM are known 2-outcome measurements. In this paper, we consider the shadow tomography problem with a potentially inaccurate prediction & rhov; of the true state rho. This corresponds to practical cases where we possess prior knowledge of the unknown state. For example, in quantum verification or calibration, we may be aware of the quantum state that the quantum device is expected to generate. However, the actual state it generates may have deviations. We introduce an algorithm with sample complexity & Otilde;(n max{parallel to rho - & rhov;parallel to 1,epsilon}log2M/epsilon 4). In the generic case, even if the prediction can be arbitrarily bad, our algorithm has the same complexity as the best algorithm without prediction [2]. At the same time, as the prediction quality improves, the sample complexity can be reduced smoothly to & Otilde;(nlog2M/epsilon 3) when the trace distance between the prediction and the unknown state is Theta(epsilon). Furthermore, we conduct numerical experiments to validate our theoretical analysis. The experiments are constructed to simulate noisy quantum circuits that reflect possible real scenarios in quantum verification or calibration. Notably, our algorithm outperforms the previous work without prediction in most settings.
关键词	shadow tomography online learning quantum state learning FTRL quantum machine learning
DOI	10.1007/s11704-024-40414-w
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[62372006] ; National Natural Science Foundation of China[92365117] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDB28000000] ; Fundamental Research Funds for the Central Universities, Peking University ; Chinese Academy of Sciences
WOS研究方向	Computer Science
WOS类目	Computer Science, Information Systems ; Computer Science, Software Engineering ; Computer Science, Theory & Methods
WOS记录号	WOS:001379549800001
出版者	HIGHER EDUCATION PRESS
引用统计
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/41059
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Zhang, Jialin
作者单位	1.Fudan Univ, Sch Data Sci, Shanghai 200433, Peoples R China 2.Chinese Acad Sci, Inst Comp Technol, State Key Lab Processors, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 101408, Peoples R China 4.Peking Univ, Ctr Frontiers Comp Studies, Beijing 100871, Peoples R China 5.Peking Univ, Sch Comp Sci, Beijing 100871, Peoples R China 6.Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Jiang, Jiyu,Wan, Zongqi,Li, Tongyang,et al. Shadow tomography of quantum states with prediction[J]. FRONTIERS OF COMPUTER SCIENCE,2025,19(7):12.
APA	Jiang, Jiyu,Wan, Zongqi,Li, Tongyang,Shao, Meiyue,&Zhang, Jialin.(2025).Shadow tomography of quantum states with prediction.FRONTIERS OF COMPUTER SCIENCE,19(7),12.
MLA	Jiang, Jiyu,et al."Shadow tomography of quantum states with prediction".FRONTIERS OF COMPUTER SCIENCE 19.7(2025):12.