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The cost functional for increasing number of initial states for a gate. Initial states are randomly distribuited inside the Bloch sphere. Gray bars are for a constant Hamiltonian. Red (dark) bars are for the optimized Hamiltonian. Damping constants are , , and .
The control fields of the optimized Hamiltonian for as obtained from the analytic method.
The control fields generated numerically by direct optimization from with harmonic starting fields. Solid line: , dashed line: , and dotted-dashed line: .
The cost functional computed with for different ratios of decay rates. Gray bars are for a constant Hamiltonian. Red (dark) bars are for the optimized version.
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