Singularities of Quantum Control Landscapes

Abstract

A quantum control landscape is defined as the objective to be optimized as a function of the control variables. Existing empirical and theoretical studies reveal that most realistic quantum control landscapes are generally devoid of false traps. However, the impact of singular controls has yet to be investigated, which can arise due to a singularity on the mapping from the control to the final quantum state. We provide an explicit characterization of such controls that are strongly Hamiltonian-dependent and investigate their associated landscape geometry. Although in principle the singularities may correspond to local traps, we did not find any in numerical simulations. Also, as they occupy a small portion of the entire set of possible critical controls, their influence is expected to be much smaller than controls corresponding to the commonly located regular extremals. This observation supports the established ease of optimal searches to find high-quality controls in simulations and experiments.

18 pages, 3 figures

References in corpus (9)

• Control of quantum phenomena: Past, present, and future
• Singular extremals for the time-optimal control of dissipative spin 1/2 particles
• Are there traps in quantum control landscapes?
• Control Landscapes for Observable Preparation with Open Quantum Systems
• Search complexity and resource scaling for the quantum optimal control of unitary transformations
• Exploring Quantum Control Landscapes: Topology, Features, and Optimization Scaling
• Optimal Control Theory for Continuous Variable Quantum Gates
• Comment on "Are There Traps in Quantum Control Landscapes?"
• The role of controllability in optimizing quantum dynamics

Cited by in corpus (34)

• Training Schrödinger's cat: quantum optimal control
• Quantum Approximate Optimization Algorithm for MaxCut: A Fermionic View
• Theory of overparametrization in quantum neural networks
• Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape
• Optimal Protocols in Quantum Annealing and QAOA Problems
• Deep Reinforcement Learning for Quantum Gate Control
• One decade of quantum optimal control in the chopped random basis
• Are there traps in quantum control landscapes?
• Exploring constrained quantum control landscapes
• Quantum Control Landscapes: A Closer Look
• A Data-Driven Gradient Algorithm for High-Precision Quantum Control
• Exploring Quantum Control Landscapes: Topology, Features, and Optimization Scaling
• Trap-free manipulation in the Landau-Zener system
• Searching for quantum optimal controls in the presence of singular critical points
• Searching for quantum optimal controls under severe constraints
• The role of controllability in optimizing quantum dynamics
• Comparison between optimal control and shortcut to adiabaticity protocols in a linear control system
• Experimental exploration over a quantum control landscape through nuclear magnetic resonance
• Geometric analysis of minimum time trajectories for a two-level quantum system
• Common Foundations of Optimal Control Across the Sciences: evidence of a free lunch
• Drawing together control landscape and tomography principles
• Optimizing QAOA: Success Probability and Runtime Dependence on Circuit Depth
• Dynamic Homotopy and Landscape Dynamical Set Topology in Quantum Control
• Limits of optimal control yields achievable with quantum controllers
• From Ansätze to Z-gates: a NASA View of Quantum Computing
• Exploring the complexity of quantum control optimization trajectories
• Minimum time control of a pair of two-level quantum systems with opposite drifts
• Phenomenon of a stronger trapping behaviour in $\Lambda$-type quantum systems with symmetry
• Control landscapes for a class of non-linear dynamical systems: sufficient conditions for the absence of traps
• Critical points of the optimal quantum control landscape: a propagator approach
• Characterization of the Critical Sets of Quantum Unitary Control Landscapes
• Minimum time generation of SU(2) transformations with asymmetric bounds on the controls
• Topology of Classical Molecular Optimal Control Landscapes in Phase Space
• Diverse efficiency of observable optimization for four-level quantum systems with higher-order traps