We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum estimation algorithms make assumptions that make them unsuitable for this 'coherent' setting, leaving only the textbook approach. We present novel algorithms for phase, energy, and amplitude estimation that are both conceptually and computationally simpler than the textbook method, featuring both a smaller query complexity and ancilla footprint. They do not require a quantum Fourier transform, and they do not require a quantum sorting network to compute the median of several estimates. Instead, they use block-encoding techniques to compute the estimate one bit at a time, performing all amplification via singular value transformation. These improved subroutines accelerate the performance of quantum Metropolis sampling and quantum Bayesian inference.

中文翻译：

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用于相位、能量和幅度估计的更快相干量子算法

我们考虑在以下条件下执行相位估计：我们只得到输入状态的一个副本，输入状态不必是酉的本征态，并且状态不能被测量。大多数量子估计算法做出的假设使它们不适合这种“相干”设置，只留下教科书的方法。我们提出了用于相位、能量和幅度估计的新算法，这些算法在概念和计算上都比教科书方法更简单，具有更小的查询复杂度和辅助足迹。它们不需要量子傅立叶变换，也不需要量子排序网络来计算多个估计的中值。相反，他们使用块编码技术一次计算一位估计，通过奇异值变换执行所有放大。这些改进的子程序可加速量子 Metropolis 采样和量子贝叶斯推理的性能。