用于PageRank计算的多步量子共振跃迁量子算法
Quantum algorithm for PageRank computation through multistep quantum resonant transitions
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中文总结 AI 辅助
提出一种基于多步量子共振跃迁的量子算法，通过构造哈密顿量演化路径，以单辅助量子比特高效获取Google矩阵PageRank向量的量子态，适用于大规模网络。
中文摘要 AI 辅助
我们提出了一种量子算法，通过多步量子共振跃迁（mQRT）获得编码Google矩阵PageRank向量的量子态。在该算法中，PageRank向量被编码在与Google矩阵相关的问题哈密顿量的基态中。通过将对应于Google矩阵的网页图划分为一系列具有嵌套结构的子图，我们基于这些子图构造一系列哈密顿量，形成从简单初始哈密顿量到问题哈密顿量的哈密顿量演化路径。通过逐步经历中间哈密顿量的基态，经由QRT获得问题哈密顿量的基态。该算法仅需一个辅助量子比特，且算法的运行时间与步数成正比。它为高效获得大规模网络PageRank向量的量子态提供了一种新途径。
英文摘要
We present a quantum algorithm for obtaining a quantum state that encodes the PageRank vector of the Google matrix through multistep quantum resonant transition (mQRT). In the algorithm, the PageRank vector is encoded in the ground state of a problem Hamiltonian associated with the Google matrix. By dividing the web graph corresponding to the Google matrix into a series of subgraphs with nested structure, we construct a sequence of Hamiltonians based on the subgraphs to form a Hamiltonian evolution path from a simple initial Hamiltonian to the problem Hamiltonian. The ground state of the problem Hamiltonian is obtained by going through ground states of the intermediate Hamiltonians via QRT step by step. This algorithm requires only one ancillary qubit, and the runtime of the algorithm is proportional to the number of steps. It provides a new way for efficiently obtaining the quantum state of the PageRank vector of large-scale networks.
发表机构
- School of Physics, Xi’an Jiaotong University（西安交通大学物理学院）
- School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
