Recently, Kieu derived a new class of time–energy uncertainty relations, which is not only formal but also suitable for evaluating the speed limit of quantum dynamics. However, when this time–energy uncertainty relation was applied to study the quantum adiabatic Grover’s search, some approximation had been done for reaching the right conclusion. That is, the final state being orthogonal to the initial state in this problem was assumed which may cause confusion, while the truth is that the overlap between these two states is indeed very small when the problem size is very big but not equal to zero exactly. In this paper, we modify the time–energy uncertainty relation of Kieu applied to two quantum evolutions of Grover’s problem, and find that the resulting computational complexities match well with the previous works on this topic but without the need of making the assumption like that in the work of Kieu.

中文翻译：

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Kieu 的时间-能量不确定性关系应用于 Grover 搜索的量子演化

最近，Kieu 推导出了一类新的时间-能量不确定性关系，它不仅形式化而且适用于评估量子动力学的速度极限。然而，当将这种时间-能量不确定性关系应用于研究量子绝热格罗弗的搜索时，为了得出正确的结论，已经做了一些近似。也就是说，在这个问题中假设最终状态与初始状态正交，这可能会引起混淆，而事实是当问题规模很大但不完全等于零时，这两个状态之间的重叠确实很小. 在本文中，我们修改了 Kieu 的时间-能量不确定性关系，应用于 Grover 问题的两个量子演化，