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 coefficients can be loaded significantly faster than in $O(\sqrt N)$ rounds of amplitude amplification, up to only $O(1)$ many. This exponential speedup translates beyond the black box case.

翻译：量子状态制备是其他较高量子算法的重要成分,例如汉密尔顿模拟,或将分布器装入量子装置,以便用于优化任务,例如机器学习。从2000年格罗佛设计的通用“黑盒”方法开始,该方法采用振幅放大法来装载由一个神器计算的系数,在要装入的振幅上出现了一系列的结果和改进,有各种附加条件,最终导致桑德斯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,我们在两个方面改进了这一常规:我们把所需的当量的当量管理费从$g美元减少到$g@log_2(g),在比精度为$g$(略微增加非克利福德操作的计算成本)中,并显示各种系数的装载速度可以大大快于美元(sqrt N)的振动量振动弹,最多为$O(1)美元。这一指数加速值可以翻译出黑盒子外的体外。