论文标题
调整定向的量子加速
Tuning for Quantum Speedup in Directed Lackadaisical Quantum Walks
论文作者
论文摘要
量子步行构成设计量子算法和信息处理任务的重要工具。在一个缺乏的行走中，除了有可能从节点中移出的可能性外，步行者还可以在同一节点上保持一定的可能性。这是通过引入自动浮动力量$ l $参数化的自浮道来实现的，该节点附在节点上，以至于大$ l $意味着助行器被困在节点上的可能性更高。在这项工作中，{\ it指示}，研究了缺乏的量子步行。根据$ L $的不同，证明存在两个政权 - 一个是古典沃克（Walker）主导的，另一个由量子助行器主导。在后一种情况下，我们还证明了两个不同的缩放机制的存在，其中$ l $在一条线上和二进制树上都存在$ l $。令人惊讶的是，大型$ L $实现了大量量子引起的加速。通过调整初始状态，可以操纵此加速的程度。
Quantum walks constitute an important tool for designing quantum algorithms and information processing tasks. In a lackadaisical walk, in addition to the possibility of moving out of a node, the walker can remain on the same node with some probability. This is achieved by introducing self-loops, parameterized by self-loop strength $l$, attached to the nodes such that large $l$ implies a higher likelihood for the walker to be trapped at the node. In this work, {\it directed}, lackadaisical quantum walks is studied. Depending on $l$, two regimes are shown to exist -- one in which classical walker dominates and the other dominated by the quantum walker. In the latter case, we also demonstrate the existence of two distinct scaling regimes with $l$ for quantum walker on a line and on a binary tree. Surprisingly, a significant quantum-induced speedup is realized for large $l$. By tuning the initial state, the extent of this speedup can be manipulated.
