Quantum algorithm for fidelity estimation

Qisheng Wang, Zhicheng Zhang, Kean Chen, Ji Guan*, Wang Fang, Junyi Liu, Mingsheng Ying

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.
Original languageEnglish
Pages (from-to)273-282
Number of pages10
JournalIEEE Transactions on Information Theory
Volume69
Issue number1
DOIs
Publication statusPublished - 5 Sept 2022

Keywords / Materials (for Non-textual outputs)

  • quantum computing
  • quantum algorithms
  • quantum fidelity
  • quantum states

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