Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search

In this work, we consider an environment formed by incoherent photons as a resource for controlling open quantum systems via control. We exploit coherent control in the Hamiltonian and dissipator which induces time-dependent decoherence rates γk(t) (via spectral density of photons) generation single-qubit gates two-level system evolves according to Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation with coefficients determined these controls. The problem is formulated minimization objective functional, sum Hilbert-Schmidt norms between four fixed basis states evolved under GKSL controls same ideal gate transformation. exact expression gradient functional respect piecewise constant obtained. Subsequent optimization performed using type algorithm adaptive step size that leads oscillating behaviour norm vs. iterations. Optimal trajectories Bloch ball various initial are computed. A relation on complex Stiefel manifolds discussed. develop methodology apply it here unitary testing example. next method non-unitary processes multi-level systems.