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 construct an optimized black box state loading scheme with which various important sets of coefficients can be loaded significantly faster than in $O(\sqrt N)$ rounds of amplitude amplification, up to only $O(1)$ many. We achieve this with two variants of our algorithm. The first employs a modification of the oracle from Sanders et al., which requires fewer ancillas ($\log_2 g$ vs $g+2$ in the bit precision $g$), and fewer non-Clifford operations per amplitude amplification round within the context of our algorithm. The second utilizes the same oracle, but at slightly increased cost in terms of ancillas ($g+\log_2g$) and non-Clifford operations per amplification round. As the number of amplitude amplification rounds enters as multiplicative factor, our black box state loading scheme yields an up to exponential speedup as compared to prior methods. This speedup translates beyond the black box case.

中文翻译：

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快速黑盒量子态准备

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，或者用于将分布加载到量子设备中以用于例如机器学习等优化任务的上下文中。从 Grover 在 2000 年设计的通用“黑匣子”方法开始，该方法采用幅度放大来加载由预言机计算的系数，在要加载的幅度上使用各种附加条件进行了一系列结果和改进，最终达到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，我们构建了一个优化的黑盒状态加载方案，使用该方案可以比在 $O(\sqrt N)$ 轮幅度放大中更快地加载各种重要的系数集，最多只有 $O(1)$ 很多. 我们通过算法的两种变体实现了这一点。第一个使用了 Sanders 等人的预言机的修改，它需要更少的辅助（$\log_2 g$ 与位精度 $g$ 中的 $g+2$），并且每个幅度放大轮内的非克利福德操作更少我们算法的上下文。第二个使用相同的预言机，但在每个放大轮的辅助 ($g+\log_2g$) 和非 Clifford 操作方面的成本略有增加。当幅度放大轮数作为乘法因子输入时，与先前的方法相比，我们的黑盒状态加载方案产生了高达指数的加速。这种加速超越了黑匣子的情况。