Quantum Algorithm for Fidelity Estimation

For two unknown mixed quantum states <inline-formula> <tex-math notation="LaTeX">\rho </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\sigma </tex-math></inline-formula> in an <inline-formula> <...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 69; no. 1; pp. 273 - 282
Main Authors: Wang, Qisheng, Zhang, Zhicheng, Chen, Kean, Guan, Ji, Fang, Wang, Liu, Junyi, Ying, Mingsheng
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Accuracy
Algorithms
Computational modeling
Computer science
Estimation
Hilbert space
Polynomials
Quantum algorithm
quantum algorithms
Quantum computers
Quantum computing
quantum fidelity
Quantum phenomena
Quantum state
quantum states
Software
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:For two unknown mixed quantum states <inline-formula> <tex-math notation="LaTeX">\rho </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\sigma </tex-math></inline-formula> in an <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-dimensional Hilbert space, computing their fidelity <inline-formula> <tex-math notation="LaTeX">F(\rho,\sigma) </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">{\mathrm{ poly}}(\log (N), r, 1/\varepsilon) </tex-math></inline-formula> time, where <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> is the lower rank of <inline-formula> <tex-math notation="LaTeX">\rho </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\sigma </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">\varepsilon </tex-math></inline-formula> is the desired precision, provided that the purifications of <inline-formula> <tex-math notation="LaTeX">\rho </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\sigma </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2022.3203985