Quantum Algorithm for Fidelity Estimation

• URL: http://arxiv.org/abs/2103.09076v2
• Date: Thu, 29 Sep 2022 03:44:45 GMT
• Title: Quantum Algorithm for Fidelity Estimation
• Authors: Qisheng Wang, Zhicheng Zhang, Kean Chen, Ji Guan, Wang Fang, Junyi Liu, Mingsheng Ying
• Abstract summary: For two unknown mixed quantum states $rho$ and $sigma$ in an $N$-dimensional space, computing their fidelity $F(rho,sigma)$ is a basic problem. We propose a quantum algorithm that solves this problem in $namepoly(log (N), r, 1/varepsilon)$ time.
• Score: 8.270684567157987
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For two unknown mixed quantum states $\rho$ and $\sigma$ in an $N$-dimensional Hilbert space, computing their fidelity $F(\rho,\sigma)$ 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 $\operatorname{poly}(\log (N), r, 1/\varepsilon)$ time, where $r$ is the lower rank of $\rho$ and $\sigma$, and $\varepsilon$ is the desired precision, provided that the purifications of $\rho$ and $\sigma$ 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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