先验知识量子搜索
Quantum search with prior knowledge
摘要：
这项工作的目的是开发一个框架，用于实现量子网络算法，使用有关网络结构的先验知识。我们寻求获得计算方法，使我们能够在量子叠加中局部确定网络特性，并相应地驱动行走行为。特别是，我们考虑一个网络，由不同类型的边缘，使节点之间的过渡导致额外的边缘相关的相移。我们结合振幅放大和相位估计，开发一种算法，探索这样的网络。在分层神经网络启发的情况下，我们得到的搜索复杂度的线性增长与指数增长的节点数。我们表明，在后果之一是能够执行量子搜索算法与指数加速相比，量子搜索，忽略了额外的相移。
英文摘要：
The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods that allows us to locally determine network properties in a quantum superposition and drive the walk behaviour accordingly. In particular, we consider a network that consists of different types of edges, such that the transitions between nodes result in extra edge-dependent phase shift. We combine amplitude amplification and phase estimation to develop an algorithm for exploring such networks. In the layered neural network inspired case we obtain linear increase of the search complexity with exponential growth of the nodes number. We show that in consequence one is able to perform quantum search algorithms with exponential speed-up compared to quantum search that neglects the extra phase shifts.
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