Optimal Quantum Algorithm for Estimating Fidelity to a Pure State
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908572600762368 |
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| author | Fang, Wang Wang, Qisheng |
| author_facet | Fang, Wang Wang, Qisheng |
| contents | 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 $\varepsilon$ by using $Θ(1/\varepsilon)$ queries to their state-preparation circuits, achieving a quadratic speedup over the folklore $O(1/\varepsilon^2)$. Our approach is technically simple, and can moreover estimate the quantity $\sqrt{\operatorname{tr}(ρσ^2)}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23650 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Quantum Algorithm for Estimating Fidelity to a Pure State Fang, Wang Wang, Qisheng Quantum Physics Information Theory 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 $\varepsilon$ by using $Θ(1/\varepsilon)$ queries to their state-preparation circuits, achieving a quadratic speedup over the folklore $O(1/\varepsilon^2)$. Our approach is technically simple, and can moreover estimate the quantity $\sqrt{\operatorname{tr}(ρσ^2)}$ 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. |
| title | Optimal Quantum Algorithm for Estimating Fidelity to a Pure State |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2506.23650 |