# Lyapunov stability analysis for invariant states of quantum systems

@article{Emzir2017LyapunovSA, title={Lyapunov stability analysis for invariant states of quantum systems}, author={M. Emzir and Ian R. Petersen and Matthew J. Woolley}, journal={2017 IEEE 56th Annual Conference on Decision and Control (CDC)}, year={2017}, pages={5505-5510} }

In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use weak convergence, in this article we analyze the convergence of density operators by considering the set of density operators as a Banach space. We show that the set of invariant density operators is both closed and convex, which implies the impossibility of…

## 3 Citations

### Stability analysis of quantum systems: A Lyapunov criterion and an invariance principle

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### Convergence to pure steady states of linear quantum systems

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This work gives compact and intuitive necessary and sufficient conditions for single-mode linear quantum systems to have pure Gaussian steady states in terms of the Hamiltonian and coupling operators.

### Quantum Switch Realization by the Quantum Lyapunov Control

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The quantum Lyapunov control scheme is presented which implements a quantum switch (it can be used as a part of future quantum networks), however, this implementation is not based on a quantum gates circuit and directly concerns the spins of the qubits which realize the quantum switch operation.

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