论文标题
基于测量的量子计算的图形状态的有效代数表示
An efficient algebraic representation for graph states for measurement-based quantum computing
论文作者
论文摘要
图状态是基于测量的计算的主要计算构建块，也是门模型体系结构中误差校正的有用工具。该图状态形成一类量子状态，这些量子状态是Abelian稳定器操作员组的特征向量。它们拥有由图形结构引起的拓扑特性，包括高度连接的节点的存在，称为集线器。从集线器节点开始，我们演示了如何通过稳定器组的发电机有效地表达图形状态。我们通过表达环和恒星拓扑来提供示例，为此，稳定器的数量分别从N到N/2和N到1。我们证明了图态可以由稳定器组的亚组生成。因此，我们提供一个代数框架，以减少稳定剂数量来操纵图状态。
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the abelian group of stabilizer operators. They own topological properties, arising from their graph structure, including the presence of highly connected nodes, called hubs. Starting from hub nodes, we demonstrate how to efficiently express a graph state through the generators of the stabilizer group. We provide examples by expressing the ring and the star topology, for which the number of stabilizers reduces from n to n/2, and from n to 1, respectively. We demonstrate that the graph states can be generated by a subgroup of the stabilizer group. Therefore, we provide an algebraic framework to manipulate the graph states with a reduced number of stabilizers.
