Matthew D. Grace, Jason Dominy, Wayne M. Witzel, Malcolm S. Carroll
Constructing high-fidelity control fields that are robust to control, system, and surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for $\pi/2$- and $\pi$-pulses, and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from $\pi/2$- and $\pi$-pulses. We systematically integrate this criteria with optimal control theory, and incorporate a system parameter estimate to produce improvements in gate fidelity and robustness, via a numerical example based on double quantum dot qubits. For the qubit model used in this work, \emph{post facto} analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.
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http://arxiv.org/abs/1105.2358
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