广义拉普拉斯量子行走的更快计算
Faster Computation with the Generalized Laplacian Quantum Walk
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中文总结 AI 辅助
本文证明由广义拉普拉斯算子驱动的连续时间量子行走，通过调节度矩阵倍数，能在接近最优时间内搜索多标记顶点的完全二分图，从而比标准量子行走更快，为开发新量子算法提供潜力。
中文摘要 AI 辅助
量子行走是经典随机行走或马尔可夫链的量子对应物。它们是量子计算的通用模型，并支撑着多种量子算法。我们证明，由广义拉普拉斯算子（可出现在自旋链中）实现的连续时间量子行走，能够比由标准拉普拉斯算子或邻接矩阵控制的典型量子行走更快地解决计算问题。该广义拉普拉斯算子由标准拉普拉斯算子加上度矩阵的实数值倍数组成，我们证明，随着度矩阵倍数幅度的增加，其对应的量子行走可以在接近最优的时间内搜索具有多个标记顶点的完全二分图。这提升了广义拉普拉斯量子行走作为开发额外更快量子算法的有用方法的潜力。
英文摘要
Quantum walks are the quantum analogues of classical random walks or Markov chains. They are universal models of quantum computing, and they underpin a variety of quantum algorithms. We prove that a continuous-time quantum walk effected by a generalized Laplacian, which can arise in spin chains, can solve a computational problem more quickly than typical quantum walks governed by the standard Laplacian or adjacency matrix. This generalized Laplacian consists of the standard Laplacian plus a real-valued multiple of the degree matrix, and we prove that as the magnitude of the multiple of the degree matrix is increased, its corresponding quantum walk can search the complete bipartite graph with multiple marked vertices in time that approaches the optimal. This raises the potential for the generalized Laplacian quantum walk to be a useful method for developing additional faster quantum algorithms.
发表机构
- Creighton University（克里顿大学）
机构由 AI 辅助整理，请以论文原文为准。
