The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem by developing a strategy to integrate the quantum phase estimation algorithm within a fully differentiable framework. This is accomplished by devising a smooth estimator able to tackle arbitrary initial states. We provide analytical expressions to characterize the statistics and algorithmic cost of this estimator. Furthermore, we provide numerical evidence that the estimation accuracy is retained when an arbitrary state is considered and that it exceeds the one of standard majority rule. We explicitly use this procedure to estimate chemically relevant quantities, demonstrating our approach through ground-state and triplet excited state geometry optimization with simulations involving up to 19 qubits. This work paves the way for new quantum algorithms that combine interference methods and quantum differentiable programming.

中文翻译：

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一种可微量子相位估计算法


电子特性的模拟是现代电子结构理论中的一个关键问题，推动了过去几十年来开发计算能量导数协议的巨大努力。在这项工作中，我们通过开发一种将量子相位估计算法集成到完全可微框架内的策略来解决这个问题。这是通过设计一个能够处理任意初始状态的平滑估计器来实现的。我们提供解析表达式来表征该估计器的统计数据和算法成本。此外，我们提供了数值证据，表明当考虑任意状态时，估计精度得以保留，并且超过了标准多数规则。我们明确地使用此过程来估计化学相关量，通过涉及多达 19 个量子位的模拟来演示我们的方法，通过基态和三重激发态几何优化。这项工作为结合干涉方法和量子可微分编程的新量子算法铺平了道路。