2026-07-23T22:37:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24472 2025-12-16T13:59:33Z ddc:004 open_access

Optimal Quantum Algorithm for Estimating Fidelity to a Pure State Fang, Wang Wang, Qisheng Quantum computing fidelity estimation quantum algorithms quantum query complexity 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 by using Θ(1/ε) queries to their state-preparation circuits, achieving a quadratic speedup over the folklore O(1/ε²). Our approach is technically simple, and can moreover estimate the quantity √{tr(ρσ²)} 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Wang Fang and Qisheng Wang 2025 Is Part Of LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2025.4 urn:nbn:de:0030-drops-244727 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.4 eng https://creativecommons.org/licenses/by/4.0/legalcode