优化 rodeo 投影
Optimizing rodeo projection
AI总结：
针对 rodeo 算法随机选取演化时间导致抑制因子呈对数正态分布且波动巨大的问题，本文提出跨指数多尺度有意选择时间，获得严格上界并将平均抑制降低多个数量级。
摘要：
rodeo 算法最近被提出，作为量子计算中一种有效方法，用于在具有离散谱的系统中将给定初始态投影到固定能量的态。在 rodeo 算法的最初表述中，这些时间是通过具有固定 RMS 时间的高斯分布随机选择的。本文表明，这种选择时间的随机方法在抑制不需要的分量方面会遭受指数级大的波动：随着迭代次数变大，由随机选择获得的抑制因子分布趋近于对数正态分布，从而导致非常大的波动。我们注意到，通过有意而非随机地选择时间，可以避免这种波动，并获得关于抑制的严格上界。此外，相对于随机算法，使用固定计算成本的平均抑制可以降低许多个数量级。实现这一点的关键是选择在指数多个时间尺度上变化的时间，从一个适中的最大尺度开始，一直下降到指数级更小的时间尺度。
英文摘要：
The rodeo algorithm has been proposed recently as an efficient method in quantum computing for projection of a given initial state onto a state of fixed energy for systems with discrete spectra. In the initial formulation of the rodeo algorithm these times were chosen randomly via a Gaussian distribution with fixed RMS times. In this paper it is shown that such a random approach for choosing times suffers from exponentially large fluctuations in the suppression of unwanted components: as the number of iterations gets large, the distribution of suppression factors obtained from random selection approaches a log-normal distribution leading to remarkably large fluctuations. We note that by choosing times intentionally rather than randomly such fluctuations can be avoided and strict upper bounds on the suppression can be obtained. Moreover, the average suppression using fixed computational cost can be reduced by many orders of magnitude relative to the random algorithm. A key to doing this is to choose times that vary over exponentially many times scales, starting from a modest maximum scale and going down to time scales exponentially smaller.
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