Singular extremals for the time-optimal control of dissipative spin 1/2 particles

Abstract

We consider the time-optimal control by magnetic fields of a spin 1/2 particle in a dissipative environment. This system is used as an illustrative example to show the role of singular extremals in the control of quantum systems. We analyze a simple case where the control law is explicitly determined. We experimentally implement the optimal control using techniques of nuclear magnetic resonance. To our knowledge, this is the first experimental demonstration of singular extremals in quantum systems with bounded control amplitudes.

10 pages, 3 figures

References in corpus (8)

• Time Optimal Control in Spin Systems
• Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
• Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field
• Optimal Control of Spin Dynamics in the Presence of Relaxation
• Boundary of Quantum Evolution under Decoherence
• Time-optimal control of a two-level dissipative quantum system
• Time-Minimal Control of Dissipative Two-level Quantum Systems: the Generic Case
• Optimal Control of Quantum Dissipative Dynamics: Analytic solution for cooling the three level $\Lambda$ system

Cited by in corpus (93)

• Control of quantum phenomena: Past, present, and future
• Training Schrödinger's cat: quantum optimal control
• Quantum control of molecular rotation
• Controlling open quantum systems: Tools, achievements, and limitations
• Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
• Gradient optimization of analytic controls: the route to high accuracy quantum optimal control
• Leakage reduction in fast superconducting qubit gates via optimal control
• Optimal trajectories for efficient atomic transport without final excitation
• Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
• Frictionless atom cooling in harmonic traps: a time-optimal approach
• Time-optimal control of SU(2) quantum operations
• Speeding up and slowing down the relaxation of a qubit by optimal control
• Robust optimal control of two-level quantum systems
• Optimal Control Methods for Quantum Batteries
• Experimental time-optimal universal control of spin qubits in solids
• Simultaneous time-optimal control of the inversion of two spin 1/2 particles
• Singularities of Quantum Control Landscapes
• Broadband 180 degree universal rotation pulses for NMR spectroscopy designed by optimal control
• Enhanced precision bound of low-temperature quantum thermometry via dynamical control
• Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance
• Local quantum control of Heisenberg spin chains
• Optimized cross-resonance gate for coupled transmon systems
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Optimal control of quantum superpositions in a bosonic Josephson junction
• Robust and highly-efficient discrimination of chiral molecules through three-mode parallel paths
• Quantum state control of a Bose-Einstein condensate in an optical lattice
• Doubly geometric quantum control
• Fast and robust control of two interacting spins
• Measurement-assisted Landau-Zener transitions
• Efficient Generation of the Triplet Bell State Between Coupled Spins Using Transitionless Quantum Driving and Optimal Control
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls
• Efficiency of quantum controlled non-Markovian thermalization
• Searching for quantum optimal controls in the presence of singular critical points
• Time-optimal selective pulses of two uncoupled spin 1/2 particles
• Time-optimal purification of a qubit in contact with a structured environment
• Multiple-spin coherence transfer in linear Ising spin chains and beyond: numerically-optimized pulses and experiments
• The tennis racket effect in a three-dimensional rigid body
• Reverse engineering protocols for controlling spin dynamics
• Comparison between optimal control and shortcut to adiabaticity protocols in a linear control system
• A fully efficient time-parallelized quantum optimal control algorithm
• Time-Optimal Adiabatic-Like Expansion of Bose-Einstein Condensates
• Control of molecular dynamics with zero-area fields: Application to molecular orientation and photofragmentation
• Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls
• Geometric analysis of minimum time trajectories for a two-level quantum system
• Approximation of Reachable Set for Coherently Controlled Open Quantum Systems: Application to Quantum State Engineering
• A discrete-pulse optimal control algorithm with an application to spin systems
• Robust control of an ensemble of springs: Application to Ion Cyclotron Resonance and two-level Quantum Systems
• Control landscape for ultrafast manipulation by a qubit
• Time optimal quantum control of two-qubit systems
• Optimal shortcuts of Stimulated Raman Adiabatic Passage in the presence of dissipation
• Optimal control and selectivity of qubits in contact with a structured environment
• The problem of coherent control in non-Markovian open quantum systems
• Optimal control of an inhomogeneous spin ensemble coupled to a cavity
• Optimal STIRAP shortcuts using the spin to spring mapping
• On the time optimal thermalization of single mode Gaussian states
• Role of control constraints in quantum optimal control
• Microscopic and phenomenological models of driven systems in structured reservoirs
• Time-optimal polarization transfer from an electron spin to a nuclear spin
• Minimum time generation of a uniform superposition in a qubit with only transverse field control
• Dissipative remote-state preparation in an interacting medium
• Optimal shape of STIRAP pulses for large dissipation at the intermediate level
• Compilation of selective pulse network on liquid-state nuclear magnetic resonance system
• A connection between optimal control theory and adiabatic passage techniques in quantum systems
• Optimal control of the signal to noise ratio per unit time for a spin 1/2 particle
• Elementary solution to the time-independent quantum navigation problem
• A greedy reconstruction algorithm for the identification of spin distribution
• Boosting Entanglement Between Exciton-Polaritons with On-Off Switching of Josephson Coupling
• Comparative study of monotonically convergent optimization algorithms for the control of molecular rotation
• Ultimate conversion efficiency bound for the forward double-$\Lambda$ atom-light coupling scheme
• Minimum time control of a pair of two-level quantum systems with opposite drifts
• Rapid quantum approaches for combinatorial optimisation inspired by optimal state-transfer
• Purity Speed Limit of Open Quantum Systems from Magic Subspaces
• A general formulation of time-optimal quantum control and optimality of singular protocols
• Quantum Pontryagin Principle under Continuous Measurements and Feedback
• Saturation of a spin 1/2 particle by generalized Local control
• Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Time-optimal universal quantum gates on superconducting circuits
• Decoherence, relaxation and chaos in a kicked-spin ensemble
• Time-optimal state transfer for an open qubit
• Exploring the limits of the generation of non-classical states of spins coupled to a cavity by optimal control
• Time Optimal Quantum Control of Spinor States
• Newton algorithm for Hamiltonian characterization in quantum control
• On the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space
• Quantum Control Landscapes Beyond the Dipole Approximation
• Minimum-Time Quantum Transport with Bounded Trap Velocity
• On the optimality of optical pumping for a closed $\Lambda$-system with large decay rates of the intermediate excited state
• Gradient flow for controlling quantum ensemble
• Minimum time generation of SU(2) transformations with asymmetric bounds on the controls
• Subsystem-based Approach to Scalable Quantum Optimal Control
• Exploring the physical limits of saturation contrast in Magnetic Resonance Imagign
• Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control
• Optimal control theory for applications in magnetic resonance imaging