量子算法设计中的控制箭头
The Majorization Arrow in Quantum Algorithm Design
摘要：
我们应用优化理论来研究迄今为止已知的量子算法，发现它们的操作方式背后有一个优化原理。Grover的算法是这个原理的一个简洁的例子，其中优化一步一步地工作，直到找到最优的目标状态。这种情况的扩展也可以在基于量子绝热演化的算法和量子相位估计算法家族中找到，包括Shor的算法。我们指出，在量子算法中，时间箭头是一个优箭头。
英文摘要：
We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.
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