Posted

Wang Fang, Qisheng Wang (Jul 01 2025).
Abstract: We present an optimal quantum algorithm for fidelity estimation between two quantum states when one of them is pure. In particular, the (square root) fidelity of a mixed state to a pure state can be estimated to within additive error ε\varepsilon by using Θ(1/ε)\Theta(1/\varepsilon) queries to their state-preparation circuits, achieving a quadratic speedup over the folklore O(1/ε2)O(1/\varepsilon^2). Our approach is technically simple, and can moreover estimate the quantity tr(ρσ2)\sqrt{\operatorname{tr}(\rho\sigma^2)} that is not common in the literature. To the best of our knowledge, this is the first query-optimal approach to fidelity estimation involving mixed states.

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