Introduction to Theoretical and Experimental aspects of Quantum Optimal Control

Abstract

Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum principle, in a physicist-friendly way. An analogy with classical Lagrangian and Hamiltonian mechanics is proposed to present the main results used in this field. Emphasis is placed on the different numerical algorithms to solve a quantum optimal control problem. Several examples ranging from the control of two-level quantum systems to that of Bose-Einstein Condensates (BEC) in a one-dimensional optical lattice are studied in detail, using both analytical and numerical methods. Codes based on shooting method and gradient-based algorithms are provided. The connection between optimal processes and the quantum speed limit is also discussed in two-level quantum systems. In the case of BEC, the experimental implementation of optimal control protocols is described, both for two-level and many-level cases, with the current constraints and limitations of such platforms. This presentation is illustrated by the corresponding experimental results.

51 pages, 15 figures, 272 references

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• Enhancing quantum exchanges between two oscillators

Cited by in corpus (36)

• Roadmap on Quantum Thermodynamics
• Fast charging of an Ising spin pair quantum battery using optimal control
• Zero- to Ultralow-field Nuclear Magnetic Resonance
• Pontus-Mpemba effects
• Quantum algorithms for scientific computing
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Robust Quantum Control via Multipath Interference for Thousandfold Phase Amplification in a Resonant Atom Interferometer
• TorchQC -- A framework for efficiently integrating machine and deep learning methods in quantum dynamics and control
• Toward a Theory of Phase Transitions in Quantum Control Landscapes
• Optimal control of a Bose-Eintein Condensate in an optical lattice: The non-linear and two-dimensional cases
• Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems
• Phenomenon of a stronger trapping behaviour in $\Lambda$-type quantum systems with symmetry
• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
• The iSWAP gate with polar molecules: Robustness criteria for entangling operations
• Quantum superpositions of current states in Rydberg-atom networks
• Parameterization and optimizability of pulse-level VQEs
• Relaxation Control of Open Quantum Systems
• Engineering the uncontrollable: Steering noisy spin-correlated radical-pairs with coherent and incoherent control
• Tackling the Challenges of Adding Pulse-level Support to a Heterogeneous HPCQC Software Stack: MQSS Pulse
• Unitary Transformations using Robust Optimal Control on a Cold Atom Qudit
• An automated geometric space curve approach for designing dynamically corrected gates
• Application of Optimal Control to Time-Resolution Protocol for Quantum Sensing
• Engineering Precise and Robust Effective Hamiltonians
• Fast chiral resolution with optimal control
• Time-optimal single-scalar control on a qubit of unitary dynamics
• Robust implicit quantum control of interacting spin chains
• Quantum optimal control of the Dicke manifold in dipolar Rydberg atom arrays
• Efficiency of optimal control for noisy spin qubits in diamond
• Diverse efficiency of observable optimization for four-level quantum systems with higher-order traps
• Optimal control over the full counting statistics in a non-adiabatic pump
• Simultaneous control of populations and coherence phase of open two-level quantum systems with a single pulse
• Fast momentum-selective transport of Bose-Einstein condensates via controlled non-adiabatic dynamics in optical lattices
• Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach
• Harnessing subspace controllability: Dynamical generation of Dicke states in Heisenberg-coupled qubit arrays with a single local control
• Entropy production versus memory effects in two-level open quantum systems
• Approaching the Quantum Speed Limit in Quantum Gates with Geometric Control