Robust Control Performance for Open Quantum Systems
- URL: http://arxiv.org/abs/2008.13691v2
- Date: Thu, 16 Jun 2022 18:16:06 GMT
- Title: Robust Control Performance for Open Quantum Systems
- Authors: Sophie G. Schirmer, Frank C. Langbein, Carrie A. Weidner, Edmond
Jonckheere
- Abstract summary: A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error.
A difficulty arising from the singularity of the closed-loop Bloch equations for the quantum state is overcome by introducing the #-inversion lemma.
Additional difficulties occur when symmetry gives rise to multiple open-loop poles, which under symmetry-breaking unfold into single eigenvalues.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Robust performance of control schemes for open quantum systems is
investigated under classical uncertainties in the generators of the dynamics
and nonclassical 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.
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