Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in quantum states. In this paper, we introduce an optimization of the inversion-by-the-mean step of the algorithm. This optimization serves two purposes: from a practical perspective, it can lead to a performance improvement; from a theoretical one, it leads to a novel interpretation of the actual nature of this step. This step is a reflection, which is realized by (a) cancelling the superposition of a general state to revert to the original all-zeros state, (b) flipping the sign of the amplitude of the all-zeros state, and finally (c) reverting back to the superposition state. Rather than canceling the superposition, our approach allows for going forward to another state that makes the reflection easier. We validate our approach on set and array search, and confirm our results experimentally on real quantum hardware.

中文翻译：

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使用 Grover 算法的广义版本优化量子搜索

Grover 搜索算法在引入时是一个突破，其幅度放大的基本过程已成为许多其他算法和模式的构建块，用于提取以量子态编码的信息。在本文中，我们介绍了算法的均值求逆步骤的优化。这种优化有两个目的：从实际角度来看，它可以带来性能提升；从理论上来说，它导致了对这一步骤的实际性质的一种新颖的解释。这一步是一个反射，通过（a）取消一个一般状态的叠加恢复到原来的全零状态，（b）翻转全零状态的幅度符号，最后（c） ) 恢复到叠加状态。我们的方法不是取消叠加，而是允许前进到另一个使反射更容易的状态。我们在集合和数组搜索上验证了我们的方法，并在真实的量子硬件上通过实验确认了我们的结果。