Quantum state preparation is an important ingredient for other higher-level quantum algorithms, such as Hamiltonian simulation, or for loading distributions into a quantum device to be used e.g. in the context of optimization tasks such as machine learning. Starting with a generic "black box" method devised by Grover in 2000, which employs amplitude amplification to load coefficients calculated by an oracle, there has been a long series of results and improvements with various additional conditions on the amplitudes to be loaded, culminating in Sanders et al.'s work which avoids almost all arithmetic during the preparation stage. In this work, we improve upon this routine in two aspects: we reduce the required qubit overhead from $g$ to $\log_2(g)$ in the bit precision $g$ (at a cost of slightly increasing the count of non-Clifford operations), and show how various sets of $N$ coefficients can be loaded significantly faster than in $O(\sqrt N)$ rounds of amplitude amplification - up to only $O(1)$ many - by bootstrapping the procedure with an optimised initial state.

中文翻译：

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快速黑盒量子状态准备

量子态准备是其他高级量子算法的重要组成部分，例如哈密顿模拟，或者将分布加载到量子设备中，例如在机器学习等优化任务的上下文中使用。从 Grover 于 2000 年设计的通用“黑匣子”方法开始，该方法对预言机计算的载荷系数采用幅度放大，已经有一系列结果和改进以及对要加载的幅度的各种附加条件，最终Sanders 等人的工作在准备阶段避免了几乎所有的算术。在这项工作中，我们在两个方面对该例程进行了改进：