There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of energies within a target energy-interval without requiring good approximations of the target energy-eigenstates. We discuss the implementation of direct and iterative amplification protocols and give resource and runtime estimates. We illustrate initial applications by amplifying excited states on molecular hydrogen.

中文翻译：

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目标区间内特征值的量子计算

计算哈密顿量的能谱，例如分析材料中的离子的光谱和能量沉积，引起了广泛的兴趣。在这项研究中，我们提出了一种量子算法，该算法对目标能量间隔内的一组能量进行采样，而无需对目标能量本征态进行很好的近似。我们讨论了直接和迭代放大协议的实现，并提供了资源和运行时估计。我们通过放大分子氢上的激发态来说明初始应用。