Constraint optimization and $\mathcal{S}\mathcal{U}(N)$ quantum control landscapes

Abstract

We develop the embedded gradient vector field method, introduced in [8] and [9], for the case of the special unitary group $\mathcal{S}\mathcal{U}(N)$ regarded as a constraint submanifold of the unitary group $\mathcal{U}(N)$. The optimization problem associated to the trace fidelity cost function defined on $\mathcal{S}\mathcal{U}(N)$ that appears in the context of $\mathcal{S}\mathcal{U}(N)$ quantum control landscapes is completely solved using the embedded gradient vector field method. We prove that for $N\ge 5$, the landscape is not $\mathcal{S}\mathcal{U}(N)$-trap free, there are always kinematic local extrema that are not global extrema.

References in corpus (24)

• Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
• Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
• Controllability of quantum mechanical systems by root space decomposition of su(N)
• Quantum Control Landscapes
• Are there traps in quantum control landscapes?
• Exploring constrained quantum control landscapes
• Quantum Control Landscapes: A Closer Look
• Riemannian preconditioning
• Gradient Flows for Optimisation and Quantum Control: Foundations and Applications
• Trap-free manipulation in the Landau-Zener system
• Riemannian Optimization on the Symplectic Stiefel Manifold
• Coherent control of a qubit is trap-free
• Adaptive regularization with cubics on manifolds
• The role of controllability in optimizing quantum dynamics
• Double-slit implementation of minimal Deutsch algorithm
• Control landscape for ultrafast manipulation by a qubit
• Common Foundations of Optimal Control Across the Sciences: evidence of a free lunch
• Geometrical dissipation for dynamical systems
• Comment on "Control landscapes are almost always trap free: a geometric assessment"
• Control of quantum transmission is trap free
• Hessian Operators on Constraint Manifolds
• Newton Algorithm on Constraint Manifolds and the 5-electron Thomson problem
• Theory of quantum control landscapes: Overlooked hidden cracks
• Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric

Cited by in corpus (4)

• Approximate encoding of quantum states using shallow circuits
• Phenomenon of a stronger trapping behaviour in $\Lambda$-type quantum systems with symmetry
• Engineering the uncontrollable: Steering noisy spin-correlated radical-pairs with coherent and incoherent control
• Diverse efficiency of observable optimization for four-level quantum systems with higher-order traps