Robust Control Performance for Open Quantum Systems

doi:10.1109/TAC.2022.3181249

Robust Control Performance for Open Quantum Systems

2022-11-01

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DOI：10.1109/TAC.2022.3181249

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Robust performance of control schemes for open quantum systems is investigated under classical uncertainties in the generators of the dynamics and non-classical uncertainties due to decoherence and initial state preparation errors. A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error to the quantum state error. This makes it possible to apply tools from classical robust control, such as structured singular value analysis. A difficulty arising from the singularity of the closed-loop Bloch equations for the quantum state is overcome by introducing the #-inversion lemma, a specialized version of the matrix inversion lemma. Under some conditions, this guarantees continuity of the structured singular value at s = 0. Additional difficulties occur when symmetry gives rise to multiple open-loop poles, which under symmetry-breaking unfold into single eigenvalues. The concepts are applied to systems subject to pure decoherence and a general dissipative system example of two qubits in a leaky cavity under laser driving fields and spontaneous emission. A nonclassical performance index, steady-state entanglement quantified by the concurrence, a nonlinear function of the system state, is introduced. Simulations confirm a conflict between entanglement, its log-sensitivity and stability margin under decoherence.

Keywords:

H-infinity control

quantum information and control

robust control

uncertain systems

Robust Control Performance for Open Quantum Systems

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