Quantum Optimal Control: Landscape Structure and Topology
arXiv:1802.05683 · doi:10.1088/1751-8121/aad657
Abstract
The core problem in optimal control theory applied to quantum systems is to determine the temporal shape of an applied field in order to maximize the expectation of value of some physical observable. The functional which maps the control field into a given value of the observable defines a Quantum Control Landscape (QCL). Studying the topological and structural features of these landscapes is of critical importance for understanding the process of finding the optimal fields required to effectively control the system, specially when external constraints are placed on both the field and the available control duration . In this work we analyze the rich structure of the of the paradigmatic Landau-Zener two-level model, studying several features of the optimized solutions, such as their abundance, spatial distribution and fidelities. We also inspect the optimization trajectories in parameter space. We are able rationalize several geometrical and topological aspects of the QCL of this simple model and the effects produced by the constraints. Our study opens the door for a deeper understanding of the QCL of general quantum systems.
References in corpus (12)
- Probing many-body dynamics on a 51-atom quantum simulator
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- Digitized adiabatic quantum computing with a superconducting circuit
- Exploring the Quantum Speed Limit with Computer Games
- Optimized pulse shapes for a resonator-induced phase gate
- The Quantum Speed Limit of Optimal Controlled Phasegates for Trapped Neutral Atoms
- Trap-free manipulation in the Landau-Zener system
- Quantum control landscape for a -atom in the vicinity of second order traps
- Controlling open quantum systems using fast transitions
- Role of control constraints in quantum optimal control
- Exploring the complexity of quantum control optimization trajectories
- Theory of quantum control landscapes: Overlooked hidden cracks
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- Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?
- Ultrafast critical ground state preparation via bang-bang protocols
- Exploring Quantum Control Landscape and Solution Space Complexity through Dimensionality Reduction & Optimization Algorithms
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- On optimization of coherent and incoherent controls for two-level quantum systems
- Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving
- On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation
- Diverse efficiency of observable optimization for four-level quantum systems with higher-order traps