Training Schrödinger's cat: quantum optimal control

Abstract

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a system from a given initial state into a desired target state with minimized expenditure of energy and resources -- as famously applied in the Apollo programme. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. --- Here state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium uniting expertise in optimal control theory and applications to spectroscopy, imaging, quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap to future developments.

31 pages; this is the starting point for a living document - we welcome feedback and discussion

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• Geometrical versus time-series representation of data in quantum control learning
• Binary Quantum Control Optimization with Uncertain Hamiltonians
• Tuning the terahertz response of liquids by creating polar many-body excitations
• An automated geometric space curve approach for designing dynamically corrected gates
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Engineering Precise and Robust Effective Hamiltonians
• Overcoming limitations on gate fidelity in noisy static exchange-coupled surface qubits
• Analytical solution of a free-fermion chain with time-dependent ramps
• Lindbladian purification
• Robustness of a universal gate set implementation in transmon systems via Chopped Random Basis optimal control
• Optimal control of photoelectron emission by realistic waveforms
• Dissipation-assisted quantum correlations in coupled qubits
• How to optimize the absorption of two entangled photons
• Linear and continuous variable spin-wave processing using a cavity-coupled atomic ensemble
• Zero- to ultralow-field nuclear magnetic resonance and its applications
• Geometric speed limit of state preparation and curved control spaces
• Quantum Control at the Boundary: an application to quantum circuits
• Swinging small quantum systems out of available values of control parameters
• Suppression of coherent errors during entangling operations in NV centers in diamond
• Engineering Strong Beamsplitter Interaction between Bosonic Modes via Quantum Optimal Control Theory
• Enhancement of superconducting pairing via quantum Lyapunov control
• Quantum Optimal Control for Pure-State Preparation Using One Initial State
• Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems
• Geometric Interpretation of Sensitivity to Structured Uncertainties in Spintronic Networks
• Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond
• Commutator-free Cayley methods
• Performance Bounds for Quantum Feedback Control
• Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control
• Globally optimal control of quantum dynamics
• Optimal control theory for applications in magnetic resonance imaging
• An obstruction to small-time controllability of the bilinear Schr{ö}dinger equation
• Small-time local controllability of the bilinear Schrödinger equation, despite a quadratic obstruction, thanks to a cubic term
• Asymptotic optimality of Grover-Radhakrishnan-Korepin algorithm
• Experimental verification of the inertial theorem control protocols
• Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Fast momentum-selective transport of Bose-Einstein condensates via controlled non-adiabatic dynamics in optical lattices
• Dipolar optimal control of entangled current states
• Iterative Linear Quadratic Regulator for Quantum Optimal Control