标题： 最优量子算法用于估计与纯态的保真度 显示英文标题

标题： Optimal Quantum Algorithm for Estimating Fidelity to a Pure State

摘要： 我们提出了一种最优的量子算法，用于估计两个量子态之间的保真度，其中一个是纯态。 特别是，通过使用$\Theta(1/\varepsilon)$次对其状态制备电路的查询，可以将混合态到纯态的（平方根）保真度估计到加法误差$\varepsilon$以内，相对于常识方法实现了二次加速$O(1/\varepsilon^2)$。 我们的方法技术上简单，并且还可以估计文献中不常见的数量$\sqrt{\operatorname{tr}(\rho\sigma^2)}$。 据我们所知，这是首次涉及混合态的保真度估计的查询最优方法。 显示英文摘要

摘要： 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 $\Theta(1/\varepsilon)$ 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 $\sqrt{\operatorname{tr}(\rho\sigma^2)}$ 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.