标题： 量子计算机上的基态和激发态能量、解析误差以及短时间演化 显示英文标题

标题： Ground and excited-state energies with analytic errors and short time evolution on a quantum computer

摘要： 准确求解薛定谔方程仍然是计算物理学、化学和材料科学中的核心挑战。 在这里，我们提出了一种基于系统自相关函数的替代本征值问题，避免直接参考波函数。 特别是，我们开发了一个严格的近似框架，使得可以从有限数量的信号样本中进行精确的频率估计。 我们的分析建立在涉及扁球谐波函数的新结果之上，并给出了误差界，这些误差界揭示了由观测时间和信号频谱密度所控制的尖锐精度过渡。 这些结果非常普遍，因此具有广泛的应用。 作为一个重要示例应用，我们考虑分子系统的量子计算。 通过将我们的谱方法与用于信号生成的量子子程序相结合，我们定义了量子扁球对角化（QPD）——一种混合经典-量子算法。 QPD在海森堡极限下同时以化学精度估计基态和激发态能量。 对不同输入状态的分析展示了该方法的鲁棒性，表明即使在状态制备不完美时，也可以保持高精度。 显示英文摘要

摘要： Accurately solving the Schr\"odinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding direct reference to a wave function. In particular, we develop a rigorous approximation framework that enables precise frequency estimation from a finite number of signal samples. Our analysis builds on new results involving prolate spheroidal wave functions and yields error bounds that reveal a sharp accuracy transition governed by the observation time and spectral density of the signal. These results are very general and thus carry far. As one important example application we consider the quantum computation for molecular systems. By combining our spectral method with a quantum subroutine for signal generation, we define quantum prolate diagonalization (QPD) - a hybrid classical-quantum algorithm. QPD simultaneously estimates ground and excited state energies within chemical accuracy at the Heisenberg limit. An analysis of different input states demonstrates the robustness of the method, showing that high precision can be retained even under imperfect state preparation.