Consensus of quantum networks with continuous-time markovian dynamics
2015 (English)In: Proceedings of the World Congress on Intelligent Control and Automation (WCICA), IEEE conference proceedings, 2015, no March, 307-312 p.Conference paper (Refereed)
In this paper, we investigate the convergence of the state of a quantum network to a consensus (symmetric) state. The state evolution of the quantum network with continuous-time swapping operators can be described by a Lindblad master equation, which also introduces an underlying interaction graph for the network. For a fixed quantum interaction graph, we prove that the state of a quantum network with continuous-time Markovian dynamics converges to a consensus state, with convergence rate given by the smallest nonzero eigenvalue of a matrix serving as the Laplacian of the quantum interaction graph. We show that this convergence rate can be optimized via standard convex programming given a fixed amount of edge weights. For switching quantum interaction graphs, we establish necessary and sufficient conditions for exponential quantum consensus and asymptotic quantum consensus, respectively. The convergence analysis is based on a bridge built between the proposed quantum consensus scheme and classical consensus dynamics, in that quantum consensus of n qubits naturally defines a consensus process on an induced classical graph with 22n nodes. Existing consensus results on classical networks can thus be adopted to establish the quantum consensus convergence.
Place, publisher, year, edition, pages
IEEE conference proceedings, 2015. no March, 307-312 p.
Quantum consensus, Quantum control, Quantum network
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-176192DOI: 10.1109/WCICA.2014.7052732ScopusID: 2-s2.0-84932165672OAI: oai:DiVA.org:kth-176192DiVA: diva2:874912
2014 11th World Congress on Intelligent Control and Automation, WCICA 2014, 29 June - 4 July 2014
QC 201511302015-11-302015-11-022015-11-30Bibliographically approved