We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Met...

中文翻译：

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优化量子相位估计以模拟哈密顿本征态

为了获得多体哈密顿量的能级，我们重新审查了量子相位估计算法，并特别注意对其输出的统计分析。我们引入与本征状态输入关联的父分布的平均相位方向，作为新的后处理工具。通过将其与未知相位联系起来，我们发现，如果将其用作未知相位的直接估计器，则它会使用少一点的分辨率就超过了标准多数规则的准确性，这显然也可以将其取反以提供无偏估计。此外，我们展示了当初始化状态为仿真传播器在整个时间演化过程中的本征态时，如何直接使用该数量精确地找到能级，从而可以使用更浅的算法。然后，我们使用IBM Q硬件对三种玩具模型进行数字量子仿真：两级系统，两旋伊辛模型和半填充时的两站点哈伯德模型。见...