In this paper, we consider the partial quantum consensus problem of a qubit network in a distributed view. The local quantum operation is designed based on the Hamiltonian by using the local information of each quantum system in a network of qubits. We construct the unitary transformation for each quantum system to achieve the partial quantum consensus, i.e., the directions of the quantum states in the Bloch ball will reach an agreement. A simple case of two-qubit quantum systems is considered first, and a minimum completing time of reaching partial consensus is obtained based on the geometric configuration of each qubit. Furthermore, we extend the approaches to deal with the more general N-qubit networks. Two partial quantum consensus protocols, based on the Lyapunov method for chain graphs and the geometry method for connected graphs, are proposed. The geometry method can be utilized to deal with more general connected graphs, while for the Lyapunov method, the global consensus can be obtained. The numerical simulation over a qubit network is demonstrated to verify the validity and the effectiveness of the theoretical results.
Emergent Problem-Graph Alignment in RL-Discovered Entanglement Topologies for QAOA
Institute for Computer Science, LMU Munich（慕尼黑大学计算机科学研究所）；relAI – Konrad Zuse School of Excellence in Reliable AI, LMU Munich（relAI – 康拉德·楚泽可靠人工智能卓越学院，慕尼黑大学）；Department of Computer Science, University of Exeter（埃克塞特大学计算机系）
Site and bond percolation thresholds in $K_{n,n}$-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies
我们估计的临界阈值的键和网站渗流非平面，有效的二维图与嵌合体拓扑结构。这些图的构建块是大小为$2n$的完全对称二部子图，称为$K_{n,n}$图。对于数值模拟，我们使用一个有效的联合发现为基础的算法，并采用有限尺寸标度分析，以获得键和网站渗流的关键属性。我们报告各自的渗透阈值为不同大小的二部子图，并验证相关的普适类是标准的二维渗透。对于D-Wave Systems Inc.~量子退火器（$n = 4$），我们根据网络脆弱性讨论设备故障，即，我们确定了在整个设备中失去大规模连接之前由于随机故障而可能不存在的量子位和耦合器的临界分数。
