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Gossip algorithm with nonuniform clock distribution: Optimization over classical and quantum networks

机译：具有非均匀时钟分布的八卦算法：古典和量子网络优化

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摘要

Distributed gossip algorithm has been studied for practical implementation of fundamental algorithms employed for collaborative processing. This paper focuses on optimizing the convergence rate of the gossip algorithm for both classical and quantum networks. By modifying the rate of the Poisson process, a new model of the gossip algorithm with nonuniform clock distribution is proposed which can reach the optimal convergence rate of the continuous-time consensus algorithm. For quantum gossip algorithm, the evolution equation of the quantum gossip algorithm is transformed to the state update equation of the classical gossip algorithm. Defining the quantum gossip operator, the original optimization problem is formulated as a convex optimization problem, where the analytical answer is provided for a series of topologies. It is shown that the optimal results obtained for uniform clock distribution are suboptimal compared to those of the nonuniform one and for nonuniform distribution the optimal answer is not unique. Based on the optimal continuous-time consensus algorithm and the detailed balance property, an effective method of obtaining one of these optimal answers is proposed.
机译：已经研究了分布式的八卦算法，用于实际实现用于协作加工的基本算法。本文侧重于优化古典和量子网络八卦算法的收敛速度。通过修改泊松过程的速率，提出了一种具有非均匀时钟分布的八卦算法的新模型，其可以达到连续时间共识算法的最佳收敛速率。对于量子八卦算法，量子八卦算法的演化方程被转换为古典八卦算法的状态更新方程。定义Quantum Gossip操作员，原始优化问题被制定为凸优化问题，其中分析答案是为一系列拓扑提供的。结果表明，与非均匀的一个和非均匀分布相比，获得均匀时钟分布的最佳结果是次优的最佳答案并不唯一。基于最佳连续时间共识算法和详细余额属性，提出了获得其中一个最佳答案之一的有效方法。

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