Stability of quantum Markov systems via Lyapunov methods in the Heisenberg picture

John Edward Gough

doi:10.1109/AUCC.2013.6697323

Stability of quantum Markov systems via Lyapunov methods in the Heisenberg picture

John Edward Gough

Department of Physics

Research output: Chapter in Book/Report/Conference proceeding › Conference Proceeding (ISBN)

Abstract

Stability of quantum Markov systems is investigated in terms of stability of invariant states. Evolutions of a quantum system in the Heisenberg picture are considered which are modeled in terms of a quantum stochastic differential equation. Using a Markov operator semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. The conditions are formulated in terms of algebraic constraints suitable for engineering quantum systems to be used in coherent feedback networks. To derive these conditions, we use quantum analogues of the stochastic Lyapunov stability theory.

Original language	English
Title of host publication	Control Conference (AUCC), 2013 3rd Australian, 2013
Publisher	Institute of Electrical and Electronics Engineers
ISBN (Print)	9781479924998
DOIs	https://doi.org/10.1109/AUCC.2013.6697323
Publication status	Published - 2013
Event	2013 3rd Australian Control Conference (AUCC 2013) - , United Kingdom of Great Britain and Northern Ireland Duration: 04 Nov 2013 → 05 Nov 2013

Conference

Conference	2013 3rd Australian Control Conference (AUCC 2013)
Country/Territory	United Kingdom of Great Britain and Northern Ireland
Period	04 Nov 2013 → 05 Nov 2013

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10.1109/AUCC.2013.6697323

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title = "Stability of quantum Markov systems via Lyapunov methods in the Heisenberg picture",

abstract = "Stability of quantum Markov systems is investigated in terms of stability of invariant states. Evolutions of a quantum system in the Heisenberg picture are considered which are modeled in terms of a quantum stochastic differential equation. Using a Markov operator semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. The conditions are formulated in terms of algebraic constraints suitable for engineering quantum systems to be used in coherent feedback networks. To derive these conditions, we use quantum analogues of the stochastic Lyapunov stability theory.",

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N2 - Stability of quantum Markov systems is investigated in terms of stability of invariant states. Evolutions of a quantum system in the Heisenberg picture are considered which are modeled in terms of a quantum stochastic differential equation. Using a Markov operator semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. The conditions are formulated in terms of algebraic constraints suitable for engineering quantum systems to be used in coherent feedback networks. To derive these conditions, we use quantum analogues of the stochastic Lyapunov stability theory.

AB - Stability of quantum Markov systems is investigated in terms of stability of invariant states. Evolutions of a quantum system in the Heisenberg picture are considered which are modeled in terms of a quantum stochastic differential equation. Using a Markov operator semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. The conditions are formulated in terms of algebraic constraints suitable for engineering quantum systems to be used in coherent feedback networks. To derive these conditions, we use quantum analogues of the stochastic Lyapunov stability theory.

UR - http://hdl.handle.net/2160/14223

U2 - 10.1109/AUCC.2013.6697323

DO - 10.1109/AUCC.2013.6697323

M3 - Conference Proceeding (ISBN)

SN - 9781479924998

BT - Control Conference (AUCC), 2013 3rd Australian, 2013

PB - Institute of Electrical and Electronics Engineers

T2 - 2013 3rd Australian Control Conference (AUCC 2013)

Y2 - 4 November 2013 through 5 November 2013

ER -

Stability of quantum Markov systems via Lyapunov methods in the Heisenberg picture

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