Growth of graph states in quantum networks

TL;DR

This paper introduces an efficient scheme for distributing complex graph states across quantum networks, accounting for noise, and analyzes the fidelity decay using classical Ising models.

Contribution

It presents a novel protocol for scalable graph state distribution in noisy quantum networks with exact fidelity calculations for specific topologies.

Findings

Fidelity can be expressed as a classical Ising model partition function.

Exact fidelity expressions for linear cluster states.

Decay rates analyzed for random graphs with arbitrary degree distributions.

Abstract

We propose a scheme to distribute graph states over quantum networks in the presence of noise in the channels and in the operations. The protocol can be implemented efficiently for large graph sates of arbitrary (complex) topology. We benchmark our scheme with two protocols where each connected component is prepared in a node belonging to the component and subsequently distributed via quantum repeaters to the remaining connected nodes. We show that the fidelity of the generated graphs can be written as the partition function of a classical Ising-type Hamiltonian. We give exact expressions of the fidelity of the linear cluster and results for its decay rate in random graphs with arbitrary (uncorrelated) degree distributions.