On optimization of coherent and incoherent controls for two-level quantum systems
arXiv:2205.02521 · doi:10.4213/im9372e
Abstract
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schrödinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation whose Hamiltonian depends on coherent control and superoperator of dissipation depends on incoherent control. For the closed system, we consider the problem for generation of the phase shift gate for some values of phases and final times for which numerically show that zero coherent control, which is a stationary point of the objective functional, is not optimal; it gives an example of subtle point for practical solving problems of quantum control. For the open system, in the two-stage method which was developed for generic N-level quantum systems in [Pechen A., Phys. Rev. A., 84, 042106 (2011)] for approximate generation of a target density matrix, here we consider the two-level systems for which modify the first ("incoherent") stage by numerically optimizing piecewise constant incoherent control instead of using constant incoherent control analytically computed using eigenvalues of the target density matrix. Exact analytical formulas are derived for the system's state evolution, the objective functions and their gradients for the modified first stage. These formulas are applied in the two-step gradient projection method. The numerical simulations show that the modified first stage's duration can be significantly less than the unmodified first stage's duration, but at the cost of optimization in the class of piecewise constant controls.
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References in corpus (38)
- Control of quantum phenomena: Past, present, and future
- Training Schrödinger's cat: quantum optimal control
- Optimal Control at the Quantum Speed Limit
- Generalized Simulated Annealing
- Controlling open quantum systems: Tools, achievements, and limitations
- Driving at the quantum speed limit: Optimal control of a two-level system
- Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
- Teaching the Environment to Control Quantum Systems
- Are there traps in quantum control landscapes?
- Time-optimal control of SU(2) quantum operations
- Time-Minimal Control of Dissipative Two-level Quantum Systems: the Generic Case
- Quantum Control Landscapes: A Closer Look
- Engineering arbitrary pure and mixed quantum states
- Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control
- Control landscapes for two-level open quantum systems
- Krotov Method for Optimal Control in Closed Quantum Systems
- Gradient Flows for Optimisation and Quantum Control: Foundations and Applications
- Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution
- Quantum Optimal Control: Landscape Structure and Topology
- Quantum Multipole Noise and Generalized Quantum Stochastic Equations
- Coherent control of a qubit is trap-free
- Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates
- Predicting quantum dynamical cost landscapes with deep learning
- Reachable sets for two-level open quantum systems driven by coherent and incoherent controls
- Quantum stochastic equation for the low density limit
- Unified analysis of terminal-time control in classical and quantum systems
- General unifying features of controlled quantum phenomena
- Optimal Design of Minimum Energy Pulses for Bloch Equations in the case of Dominant Transverse Relaxation
- Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls
- Quantum stochastic equation for test particle interacting with dilute Bose gas
- Control landscape for ultrafast manipulation by a qubit
- Energy control in a quantum oscillator using coherent control and engineered environment
- Comment on "Control landscapes are almost always trap free: a geometric assessment"
- Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach
- Incoherent control of optical signals; quantum heat engine approach
- On extrema of the objective functional for short-time generation of single qubit quantum gates
- The multi-time correlation functions, free white noise, and the generalized Poisson statistics in the low density limit
- On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation