Quantum Clique Gossiping

Bo Li,Hongsheng Qi,Junfeng Wu,Shuang Li

doi:10.1038/s41598-018-21069-7

Abstract

This paper establishes a framework of quantum clique gossiping by introducing local clique operations to networks of interconnected qubits. Cliques are local structures in complex networks being complete subgraphs, which can be used to accelerate classical gossip algorithms. Based on cyclic permutations, clique gossiping leads to collective multi-party qubit interactions. We show that at reduced states, these cliques have the same acceleration effects as their roles in accelerating classical gossip algorithms. For randomized selection of cliques, such improved rate of convergence is precisely characterized. On the other hand, the rate of convergence at the coherent states of the overall quantum network is proven to be decided by the spectrum of a mean-square error evolution matrix. Remarkably, the use of larger quantum cliques does not necessarily increase the speed of the network density aggregation, suggesting quantum network dynamics is not entirely decided by its classical topology.

Highlights

This paper establishes a framework of quantum clique gossiping by introducing local clique operations to networks of interconnected qubits
For a local complete subgraph over such networks, cyclic permutations are used to define their collective interactions which can be physically realized by a series of local environments
We have established a framework for the acceleration of quantum gossip algorithms by introducing clique operations based on cyclic permutations

Summary

Introduction

This paper establishes a framework of quantum clique gossiping by introducing local clique operations to networks of interconnected qubits. Cliques are local structures in complex networks being complete subgraphs, which can be used to accelerate classical gossip algorithms. Consensus can be defined over a set of different notions[1], but using the idea of classical gossip algorithms[9] quantum consensus algorithms can be developed with conceptual consistency. The rate of convergence of the network coherent states is established via the spectrum of a mean-square error evolution matrix. Explicit calculation of such matrix seems to be extremely difficult, the effect of cliques on the coherent states can be seen via numerical examples.

Objectives

Methods

Results

Conclusion