Diverse efficiency of observable optimization for four-level quantum systems with higher-order traps

Abstract

In this work, we perform an analytical and numerical analysis of quantum landscapes for controlling special four-level quantum systems for which we prove that the null control is a five-order trap: a $V-V$ system and an anharmonic system. As a control goal, an observable optimization is considered. The rigorous theoretical analysis is followed by the numerical experiments based on the GRadient Ascent Pulse Engineering (GRAPE) algorithm and Gradient Projection Method (GPM), performed to investigate the behavior of the efficiency of optimization for unconstrained (using GRAPE) and constrained (using GPM) controls. As the main result, we observe an interesting phenomenon with a diverse behavior of the optimization efficiency depending on the system Hamiltonian -- sharp increase of the optimization efficiency up to 100% at certain distance from the null control for a V-V system, while much slower and less significant increase (and even small decrease) for a system with the chain interaction. This sharp difference might be related with the fine structure of the subspace of controls where second derivative of the objective functional is zero.

This work is original preprint. Published version was significantly extended

References in corpus (35)

• Control of quantum phenomena: Past, present, and future
• Chopped random-basis quantum optimization
• Controlling open quantum systems: Tools, achievements, and limitations
• Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
• Quantum telecommunication based on atomic cascade transitions
• Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape
• Model-Free Quantum Control with Reinforcement Learning
• Are there traps in quantum control landscapes?
• Phase-dependent interaction in a 4-level atomic configuration
• Evolutionary Algorithms for Hard Quantum Control
• Quantum Control Landscapes: A Closer Look
• Constraints on relaxation rates for N-level quantum systems
• Singularities of Quantum Control Landscapes
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Gradient Flows for Optimisation and Quantum Control: Foundations and Applications
• Trap-free manipulation in the Landau-Zener system
• Steering the optimization pathway in the control landscape using constraints
• Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution
• Quantum Optimal Control: Landscape Structure and Topology
• Quantum control landscape for a $\Lambda$-atom in the vicinity of second order traps
• Fast Route to Thermalization
• Hessian-based optimization of constrained quantum control
• Reachable sets for two-level open quantum systems driven by coherent and incoherent controls
• Predicting quantum dynamical cost landscapes with deep learning
• Broken symmetry in a two-qubit quantum control landscape
• Exploring Quantum Control Landscape Structure
• Quantum Control Landscape of Bipartite Systems
• Exploring Quantum Control Landscape and Solution Space Complexity through Dimensionality Reduction & Optimization Algorithms
• Higher order traps for some strongly degenerate quantum control systems
• Fast generation of entanglement between coupled spins using optimization and deep learning methods
• Toward a Theory of Phase Transitions in Quantum Control Landscapes
• Phenomenon of a stronger trapping behaviour in $\Lambda$-type quantum systems with symmetry
• Constraint optimization and $\mathcal{S}\mathcal{U}(N)$ quantum control landscapes
• Gradient projection method for constrained quantum control
• Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems