用二项式Grover算法优化量子搜索
Optimizing Quantum Search with a Binomial Version of Grover's Algorithm
摘要：
幅度放大-Grover搜索算法的关键组成部分-使用迭代方法系统地增加一个或多个目标状态的概率。我们提出了新的策略，以提高扩增过程中的状态划分成类，其概率增加在不同的水平之前或期间的扩增。分配过程基于二项分布。如果预先知道搜索目标状态所属的类别，则与标准版本相比，幅度放大算法中的迭代次数可以大幅减少。在更可能的情况下，相关的类是事先不知道的，它们的选择可以在运行时配置，或者可以采用随机方法，类似于经典算法，如二分搜索。特别是，我们在前面介绍的量子字典模式的上下文中应用这种方法，其中键和值被编码在两个单独的寄存器中，并且值编码方法与键寄存器中使用的叠加类型无关。我们认为这种类型的结构是搜索的自然设置。我们证实了我们的新方法的有效性，通过在真实的量子硬件，霍尼韦尔系统模型H 0捕获离子量子计算机上获得的实验结果。
英文摘要：
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification procedure by partitioning the states into classes, whose probabilities are increased at different levels before or during amplification. The partitioning process is based on the binomial distribution. If the classes to which the search target states belong are known in advance, the number of iterations in the Amplitude Amplification algorithm can be drastically reduced compared to the standard version. In the more likely case in which the relevant classes are not known in advance, their selection can be configured at run time, or a random approach can be employed, similar to classical algorithms such as binary search. In particular, we apply this method in the context of our previously introduced Quantum Dictionary pattern, where keys and values are encoded in two separate registers, and the value-encoding method is independent of the type of superposition used in the key register. We consider this type of structure to be the natural setup for search. We confirm the validity of our new approach through experimental results obtained on real quantum hardware, the Honeywell System Model H0 trapped-ion quantum computer.
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