Quantum Algorithm for Fidelity Estimation

Wang, Q; Zhang, Z; Chen, K; Guan, J; Fang, W; Liu, J; Ying, M

Quantum Algorithm for Fidelity Estimation

Wang, Q Zhang, Z

Chen, K Guan, J Fang, W Liu, J Ying, M

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Publisher:: Institute of Electrical and Electronics Engineers (IEEE)
Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2023, 69, (1), pp. 273-282
Issue Date:: 2023-01-01

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Field	Value	Language
dc.contributor.author	Wang, Q
dc.contributor.author	Zhang, Z https://orcid.org/0000-0002-7436-0426
dc.contributor.author	Chen, K
dc.contributor.author	Guan, J
dc.contributor.author	Fang, W
dc.contributor.author	Liu, J
dc.contributor.author	Ying, M https://orcid.org/0000-0003-4847-702X
dc.date.accessioned	2023-02-22T04:32:35Z
dc.date.available	2023-02-22T04:32:35Z
dc.date.issued	2023-01-01
dc.identifier.citation	IEEE Transactions on Information Theory, 2023, 69, (1), pp. 273-282
dc.identifier.issn	0018-9448
dc.identifier.issn	1557-9654
dc.identifier.uri	http://hdl.handle.net/10453/166314
dc.description.abstract	For two unknown mixed quantum states ρ and σ in an N-dimensional Hilbert space, computing their fidelity F (ρ, σ) is a basic problem with many important applications in quantum computing and quantum information, for example verification and characterization of the outputs of a quantum computer, and design and analysis of quantum algorithms. In this paper, we propose a quantum algorithm that solves this problem in poly(log(N), r, 1/ϵ) time, where r is the lower rank of ρ and σ, and ϵ is the desired precision, provided that the purifications of ρ and σ are prepared by quantum oracles. This algorithm exhibits an exponential speedup over the best known algorithm (based on quantum state tomography) which has time complexity polynomial in N.
dc.language	en
dc.publisher	Institute of Electrical and Electronics Engineers (IEEE)
dc.relation	National Natural Science Foundation of China61832015
dc.relation.ispartof	IEEE Transactions on Information Theory
dc.relation.isbasedon	10.1109/TIT.2022.3203985
dc.rights	info:eu-repo/semantics/embargoedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies
dc.subject.classification	Networking & Telecommunications
dc.title	Quantum Algorithm for Fidelity Estimation
dc.type	Journal Article
utslib.citation.volume	69
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	1005 Communications Technologies
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
utslib.copyright.status	embargoed	*
utslib.copyright.embargo	2025-01-01T00:00:00+1000Z
dc.date.updated	2023-02-22T04:32:33Z
pubs.issue	1
pubs.publication-status	Published
pubs.volume	69
utslib.citation.issue	1

Abstract:

For two unknown mixed quantum states ρ and σ in an N-dimensional Hilbert space, computing their fidelity F (ρ, σ) is a basic problem with many important applications in quantum computing and quantum information, for example verification and characterization of the outputs of a quantum computer, and design and analysis of quantum algorithms. In this paper, we propose a quantum algorithm that solves this problem in poly(log(N), r, 1/ϵ) time, where r is the lower rank of ρ and σ, and ϵ is the desired precision, provided that the purifications of ρ and σ are prepared by quantum oracles. This algorithm exhibits an exponential speedup over the best known algorithm (based on quantum state tomography) which has time complexity polynomial in N.

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http://hdl.handle.net/10453/166314