Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls
arXiv:1909.09400 · doi:10.1007/s10773-019-04149-w
Abstract
The article considers a two-level open quantum system whose dynamics is driven by a combination of coherent and incoherent controls. Coherent control enters into the Hamiltonian part of the dynamics whereas incoherent control enters into the dissipative part. The goal is to find controls which move the system from an initial density matrix to a given target density matrix as fast as possible. To achieve this goal, we reformulate the optimal control problem in terms of controlled evolution in the Bloch ball and then apply Pontryagin maximum principle and gradient projection method to numerically find minimal time and optimal coherent and incoherent controls. General method is provided and several examples of initial and target states are explicitly considered.
arXiv commentInternat. J. Theoret. Phys. (2019)
References in corpus (13)
- Control of quantum phenomena: Past, present, and future
- Training Schrödinger's cat: quantum optimal control
- Quantum control theory and applications: A survey
- Optimal Control at the Quantum Speed Limit
- Chopped random-basis quantum optimization
- Controlling open quantum systems: Tools, achievements, and limitations
- Singular extremals for the time-optimal control of dissipative spin 1/2 particles
- Loading a Bose-Einstein Condensate onto an Optical Lattice: an Application of Optimal Control Theory to The Non Linear Schrödinger Equation
- Teaching the Environment to Control Quantum Systems
- Engineering arbitrary pure and mixed quantum states
- Measurement-assisted Landau-Zener transitions
- Active beam splitting attack applied to differential phase shift quantum key distribution protocol
- Squaring parametrization of constrained and unconstrained sets of quantum states
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