Exploiting Landscape Geometry to Enhance Quantum Optimal Control
arXiv:1911.07105 · doi:10.1103/PhysRevA.101.023410
Abstract
The successful application of Quantum Optimal Control (QOC) over the past decades unlocked the possibility of directing the dynamics of quantum systems. Nevertheless, solutions obtained from QOC algorithms are usually highly irregular, making them unsuitable for direct experimental implementation. In this paper, we propose a method to reshape those unattractive optimal controls. The approach is based on the fact that solutions to QOC problems are not isolated policies but constitute multidimensional submanifolds of control space. This was originally shown for finite-dimensional systems. Here, we analytically prove that this property is still valid in a continuous variable system. The degenerate subspace can be effectively traversed by moving in the null subspace of the hessian of the cost function, allowing for the pursuit of secondary objectives. To demonstrate the usefulness of this procedure, we apply the method to smooth and compress optimal protocols in order to meet laboratory demands.
8 pages, 2 figures
References in corpus (24)
- Quantum Simulation
- Probing many-body dynamics on a 51-atom quantum simulator
- Shortcuts to adiabaticity: concepts, methods, and applications
- Control of quantum phenomena: Past, present, and future
- Training Schrödinger's cat: quantum optimal control
- Fast optimal frictionless atom cooling in harmonic traps
- The European Quantum Technologies Roadmap
- Shortcuts to adiabaticity by counter-diabatic driving
- Single ion heat engine with maximum efficiency at maximum power
- Digitized adiabatic quantum computing with a superconducting circuit
- The quantum harmonic Otto cycle
- Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape
- Exploring the Quantum Speed Limit with Computer Games
- Frictionless atom cooling in harmonic traps: a time-optimal approach
- Exploring constrained quantum control landscapes
- Remote optimization of an ultra-cold atoms experiment by experts and citizen scientists
- Trap-free manipulation in the Landau-Zener system
- Quantum Optimal Control: Landscape Structure and Topology
- Exploring the top and bottom of the quantum control landscape
- Not quite free shortcuts to adiabaticity
- Smooth optimal control with Floquet theory
- Comparison between optimal control and shortcut to adiabaticity protocols in a linear control system
- Enhancing quantum control by improving shape pulse generation
- Optimal quantum control with digitized Quantum Annealing
Cited by in corpus (19)
- Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
- Theory of overparametrization in quantum neural networks
- Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
- Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
- Quantum metrology in a non-Markovian quantum evolution
- Predicting quantum dynamical cost landscapes with deep learning
- Optimal control of families of quantum gates
- Effects of noise on the overparametrization of quantum neural networks
- K-GRAPE: A Krylov Subspace approach for the efficient control of quantum many-body dynamics
- Robust population inversion in three-level systems by composite pulses
- Connection between inverse engineering and optimal control in shortcuts to adiabaticity
- Nonadiabatic energy fluctuations of scale-invariant quantum systems in a time-dependent trap
- Minimum time generation of a uniform superposition in a qubit with only transverse field control
- Exploring Quantum Control Landscape and Solution Space Complexity through Dimensionality Reduction & Optimization Algorithms
- Quantum control landscape for generation of and gates in an open qubit with both coherent and environmental drive
- Navigating on Quantum Control Solution Subspaces
- Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
- Quantum geometric protocols for fast high-fidelity adiabatic state transfer
- Geometry and quantum brachistochrone analysis of multiple entangled spin-1/2 particles under all-range Ising interaction