Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems
arXiv:2503.11830 · doi:10.1103/rn5j-kjq3
Abstract
We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This reduction leads to a complete analytical derivation of the optimal solution in terms of elliptic functions and elliptic integrals. Necessary optimality conditions are then obtained for the original system. These conditions are verified numerically and lead to the optimal control protocol. Various examples, ranging from state-to-state transfer to the generation of a Not gate, illustrate this study. The connection with other geometric optimization approaches that have been used to solve this problem is also discussed.
arXiv comment30 pages, 7 figures
References in corpus (39)
- Shortcuts to adiabaticity: concepts, methods, and applications
- Control of quantum phenomena: Past, present, and future
- Training Schrödinger's cat: quantum optimal control
- Time Optimal Control in Spin Systems
- Optimally robust shortcuts to population inversion in two-level quantum systems
- Quantum control of molecular rotation
- Robust quantum control by shaped pulse
- Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
- Driving at the quantum speed limit: Optimal control of a two-level system
- Monotonically convergent optimization in quantum control using Krotov's method
- Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
- Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field
- Singular extremals for the time-optimal control of dissipative spin 1/2 particles
- Introduction to Quantum Optimal Control for Quantum Sensing with Nitrogen-Vacancy Centers in Diamond
- Correction of Arbitrary Errors in Population Inversion of Quantum Systems by Universal Composite Pulses
- Optimal control of complex atomic quantum systems
- Optimal quantum control of Bose Einstein condensates in magnetic microtraps
- Time-optimal control of SU(2) quantum operations
- Robust control of quantum gates via sequential convex programming
- Robust optimal control of two-level quantum systems
- Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
- Geometric formalism for constructing arbitrary single-qubit dynamically corrected gates
- Quantum state control of a Bose-Einstein condensate in an optical lattice
- The fastest pulses that implement dynamically corrected gates
- Relaxation Optimized Transfer of Spin Order in Ising Spin Chains
- Time-optimal control of a dissipative qubit
- Multiple-spin coherence transfer in linear Ising spin chains and beyond: numerically-optimized pulses and experiments
- Time-optimal selective pulses of two uncoupled spin 1/2 particles
- Optimal Floquet Engineering for Large Scale Atom Interferometers
- Robust Control of Unstable Non-linear Quantum Systems
- Optimal Design of Minimum Energy Pulses for Bloch Equations in the case of Dominant Transverse Relaxation
- Fast charging of an Ising spin pair quantum battery using optimal control
- Pontryagin-Optimal Control of a non-Hermitian Qubit
- Statistically Characterising Robustness and Fidelity of Quantum Controls and Quantum Control Algorithms
- Minimum time generation of a uniform superposition in a qubit with only transverse field control
- Preparing Schrödinger cat states in a microwave cavity using a neural network
- Robustness of Controlled Quantum Dynamics
- Optimal control and ultimate bounds of 1:2 nonlinear quantum systems
- TorchQC -- A framework for efficiently integrating machine and deep learning methods in quantum dynamics and control
Cited by in corpus (3)
- 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
- Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach