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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| Vydáno v: | IEEE transactions on information theory Ročník 69; číslo 1; s. 273 - 282 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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IEEE
01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | 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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| AbstractList | 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>. For two unknown mixed quantum states [Formula Omitted] and [Formula Omitted] in an [Formula Omitted]-dimensional Hilbert space, computing their fidelity [Formula Omitted] 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 [Formula Omitted] time, where [Formula Omitted] is the lower rank of [Formula Omitted] and [Formula Omitted], and [Formula Omitted] is the desired precision, provided that the purifications of [Formula Omitted] and [Formula Omitted] 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 [Formula Omitted]. |
| Author | Wang, Qisheng Zhang, Zhicheng Liu, Junyi Guan, Ji Chen, Kean Fang, Wang Ying, Mingsheng |
| Author_xml | – sequence: 1 givenname: Qisheng orcidid: 0000-0001-5107-8279 surname: Wang fullname: Wang, Qisheng email: qishengwang1994@gmail.com organization: Department of Computer Science and Technology, Tsinghua University, Beijing, China – sequence: 2 givenname: Zhicheng orcidid: 0000-0002-7436-0426 surname: Zhang fullname: Zhang, Zhicheng email: iszczhang@gmail.com organization: Centre for Quantum Software and Information, University of Technology Sydney, Ultimo, NSW, Australia – sequence: 3 givenname: Kean orcidid: 0000-0002-0772-6635 surname: Chen fullname: Chen, Kean email: chenka@ios.ac.cn organization: State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China – sequence: 4 givenname: Ji orcidid: 0000-0002-3490-0029 surname: Guan fullname: Guan, Ji email: guanj@ios.ac.cn organization: State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China – sequence: 5 givenname: Wang orcidid: 0000-0001-7628-1185 surname: Fang fullname: Fang, Wang email: fangw@ios.ac.cn organization: State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China – sequence: 6 givenname: Junyi orcidid: 0000-0001-5715-4885 surname: Liu fullname: Liu, Junyi email: liujy@ios.ac.cn organization: State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China – sequence: 7 givenname: Mingsheng orcidid: 0000-0003-4847-702X surname: Ying fullname: Ying, Mingsheng email: yingms@ios.ac.cn organization: Department of Computer Science and Technology, Tsinghua University, Beijing, China |
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| Snippet | For two unknown mixed quantum states <inline-formula> <tex-math notation="LaTeX">\rho </tex-math></inline-formula> and <inline-formula> <tex-math... For two unknown mixed quantum states [Formula Omitted] and [Formula Omitted] in an [Formula Omitted]-dimensional Hilbert space, computing their fidelity... |
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| SubjectTerms | 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 |
| Title | Quantum Algorithm for Fidelity Estimation |
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