Quantum state discrimination and quantum walks

这个提议是关于量子行走和量子态鉴别的。一项初步研究表明，应该可以通过对量子游走（经典随机游走的量子版本）的输出状态应用明确的状态歧视来区分不同类型的图，量子游走可以发生在任意图上。将使用散射量子行走，其中进行行走的粒子驻留在图的边缘上，并且在每个时间步长在顶点处散射。图上的量子搜索将被研究，以找出找到一个独特的顶点所需的步骤数量如何取决于图的结构。一个目标是确定一个独特的顶点的存在如何影响图的S矩阵，以及这是否可以用来检测一个独特的顶点的存在。另一个目标是通过将它们并行放置到更大的图中来比较图。理论研究将在量子态鉴别领域进行，这是量子信息和量子计算的一个新兴领域。为了区分两个已知的量子态，可以将这些状态硬连线到区分设备中。然而，当两个完全未知的状态以某种形式的程序提供给状态机时，区分这两个状态是可能的[J. Bergou和M. Hillery，PRL 94，160501（2005）]。可编程状态鉴别器将被检查，以优化量子计算机的读出，用于操作员测试和量子算法。他们的光学实现和连接到混合量子态的歧视将被研究。这一建议的更广泛影响将是研究生和博士后的培训。

This proposal is about quantum walks and about quantum state discrimination. A preliminary study indicates that it should be possible to distinguish between different types of graphs by applying unambiguous state discrimination to the output state of a quantum walk (a quantum version of a classical random walk), which can take place on an arbitrary graph. The scattering quantum walk will be used, in which the particle making the walk resides on the edges of the graph, and scatters at the vertices at each time step. Quantum searches on graphs will be studied in order to find how the number of steps necessary to find a distinguished vertex depends on the structure of the graph. One goal is to determine how the presence of a distinguished vertex affects the S matrix of a graph, and whether this can be used to detect the presence of a distinguished vertex. Another goal is to compare graphs by placing them in parallel into a larger graph. Theoretical research will be done in the area of quantum state discrimination, an emerging subfield in quantum information and quantum computing. To discriminate two known quantum states the states can be hard-wired into the discriminating device. It is possible, however, to discriminate two completely unknown states when the states are provided in some form of program for the state discriminator [J. Bergou and M. Hillery, PRL 94, 160501 (2005)]. Programmable state discriminators will be examined in order to optimize the read-out of quantum computers for applications to operator testing and quantum algorithms. Their optical implementations and connection to the discrimination of mixed quantum states will be studied. The broader impact of this proposal will be in the training of graduate students and postdocs.