Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks

Daniel Burgarth*, Domenico D'Alessandro, Leslie Hogben, Simone Severini, Michael Young

*Awdur cyfatebol y gwaith hwn

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

51 Dyfyniadau (Scopus)
183 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Our main result says that controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions. We also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property; if a set of vertices is a zero forcing set, the associated dynamical system is controllable. These results open up the possibility of further exploiting the analogy between networks, linear control systems theory, and quantum systems Lie algebraic theory. This study is motivated by several quantum systems currently under study, including continuous quantum walks modeling transport phenomena.

Iaith wreiddiolSaesneg
Tudalennau (o-i)2349-2354
Nifer y tudalennau6
CyfnodolynIEEE Transactions on Automatic Control
Cyfrol58
Rhif cyhoeddi9
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - Medi 2013

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