Significant effort in applied quantum computing has been devoted to the problem of ground state energy estimation for molecules and materials. Yet, for many applications of practical value, additional properties of the ground state must be estimated. These include Green's functions used to compute electron transport in materials and the one-particle reduced density matrices used to compute electric dipoles of molecules. In this paper, we propose a quantum-classical hybrid algorithm to efficiently estimate such ground state properties with high accuracy using low-depth quantum circuits. We provide an analysis of various costs (circuit repetitions, maximal evolution time, and expected total runtime) as a function of target accuracy, spectral gap, and initial ground state overlap. This algorithm suggests a concrete approach to using early fault tolerant quantum computers for carrying out industry-relevant molecular and materials calculations.

中文翻译：

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用早期的容错量子计算机计算基态属性

应用量子计算的重大努力一直致力于分子和材料的基态能量估计问题。然而，对于许多具有实际价值的应用，必须估计基态的附加特性。这些包括用于计算材料中电子传输的格林函数和用于计算分子电偶极子的单粒子降低密度矩阵。在本文中，我们提出了一种量子经典混合算法，以使用低深度量子电路以高精度有效地估计此类基态特性。我们提供了对各种成本（电路重复、最大演化时间和预期总运行时间）的分析，作为目标精度、光谱间隙和初始基态重叠的函数。