Exploring constrained quantum control landscapes

Abstract

The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls. The control landscape can be shown to contain no suboptimal trapping extrema upon satisfaction of reasonable physical assumptions, but this topological analysis does not hold when significant constraints are placed on the control resources. This work employs simulations to explore the topology and features of the control landscape for pure-state population transfer with a constrained class of control fields. The fields are parameterized in terms of a set of uniformly spaced spectral frequencies, with the associated phases acting as the controls. Optimization results reveal that the minimum number of phase controls necessary to assure a high yield in the target state has a special dependence on the number of accessible energy levels in the quantum system, revealed from an analysis of the first- and second-order variation of the yield with respect to the controls. When an insufficient number of controls and/or a weak control fluence are employed, trapping extrema and saddle points are observed on the landscape. When the control resources are sufficiently flexible, solutions producing the globally maximal yield are found to form connected `level sets' of continuously variable control fields that preserve the yield. These optimal yield level sets are found to shrink to isolated points on the top of the landscape as the control field fluence is decreased, and further reduction of the fluence turns these points into suboptimal trapping extrema on the landscape. Although constrained control fields can come in many forms beyond the cases explored here, the behavior found in this paper is illustrative of the impacts that constraints can introduce.

10 figures

References in corpus (3)

• Shaped-pulse optimisation of coherent soft-x-rays
• Are there traps in quantum control landscapes?
• Tailoring laser pulses with spectral and fluence constraints using optimal control theory

Cited by in corpus (46)

• Controlling open quantum systems: Tools, achievements, and limitations
• Theory of overparametrization in quantum neural networks
• Introduction to Quantum Optimal Control for Quantum Sensing with Nitrogen-Vacancy Centers in Diamond
• Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape
• One decade of quantum optimal control in the chopped random basis
• An information theoretical analysis of quantum optimal control
• Robust control of quantum gates via sequential convex programming
• Glassy Phase of Optimal Quantum Control
• Learning quantum data with the quantum Earth Mover's distance
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Krotov Method for Optimal Control in Closed Quantum Systems
• Optimizing for an arbitrary perfect entangler. II. Application
• Steering the optimization pathway in the control landscape using constraints
• Hybrid Optimization Schemes for Quantum Control
• Quantum Optimal Control: Landscape Structure and Topology
• Achieving robust and high-fidelity quantum control via spectral phase optimization
• Characterization of control noise effects in optimal quantum unitary dynamics
• Searching for quantum optimal controls in the presence of singular critical points
• Exploiting Landscape Geometry to Enhance Quantum Optimal Control
• Searching for quantum optimal controls under severe constraints
• Deep reinforcement learning for quantum Hamiltonian engineering
• Smooth optimal control with Floquet theory
• Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice
• Experimental exploration over a quantum control landscape through nuclear magnetic resonance
• K-GRAPE: A Krylov Subspace approach for the efficient control of quantum many-body dynamics
• Exploring Quantum Control Landscape Structure
• Optimizing quantum control pulses with complex constraints and few variables through Tensorflow
• Common Foundations of Optimal Control Across the Sciences: evidence of a free lunch
• Optimal control theory with arbitrary superpositions of waveforms
• Optimizing adiabatic quantum pathways via a learning algorithm
• Searching for an optimal control in the presence of saddles on the quantum mechanical observable landscape
• Limits of optimal control yields achievable with quantum controllers
• Information Theoretical Limits for Quantum Optimal Control Solutions: Error Scaling of Noisy Channels
• Enhancement of quantum speed limit time due to cooperative effects in multilevel systems
• Information flow and error scaling for fully-quantum control
• Time-optimal control fields for quantum systems with multiple avoided crossings
• Navigating on Quantum Control Solution Subspaces
• Constraint optimization and $\mathcal{S}\mathcal{U}(N)$ quantum control landscapes
• Characterization of overparametrization in the simulation of realistic quantum systems
• Minimal Time Robust Control for Two Superconducting Qubits
• Quantum optimal control within the rotating wave approximation
• Bringing Quantum Systems under Control: A Tutorial Invitation to Quantum Computing and Its Relation to Bilinear Control Systems
• Global phase and minimum time of quantum Fourier transform for qudits represented by quadrupole nuclei
• Theory of quantum control landscapes: Overlooked hidden cracks
• Quantum Control Landscapes Beyond the Dipole Approximation
• A new way to accelerate the D-MORPH method to search for optimal quantum control