Optimal control of spin dynamics

Dominique Sugny

Juan J. Omiste, Ignacio R. Solá

Standard Quantum Optimal Control (QOC) protocols typically maximize a physical objective just at a final target time. However, tracking or measuring the quantum state during the time evolution requires the control at intermediate stages of their evolution. In this work, we extend QOC to accommodate the simultaneous optimization of observables at arbitrary intermediate times. Using a variational approach, we show that intermediate observations induce discontinuities in the costate trajectory, which can be handled with a Krotov algorithm leading to monotonic optimization and convergent results in the limit of zero temporal measurement windows. We apply this multi-time formulation to a Heisenberg XXX spin chain to control the propagation, including field-free revivals, of a Dicke state excitation. Our results demonstrate that simultaneous optimization of the same observable reshapes the driving field to balance intermediate targets with final populations. Finally, we show how this framework enables dynamic tracking of spin excitations and the active manipulation of post-pulse quantum state revivals.

Seth Merkel, Souma Chaudhury, Andrew Silberfarb +3 more

Chen Yaofeng, Li You

Abstract Quantum optimal control (QOC) relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems. Taking an unknown collective spin system as an example, this work introduces a machine-learning-based, data-driven scheme to overcome the challenges encountered, with a trained neural network (NN) assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system. The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions, remaining robust across varying system sizes and pulse durations.

Xiaodong Yang, Yunrui Ge, Bo Zhang +1 more

High-fidelity control of quantum systems is crucial for quantum information processing, but is often limited by perturbations from the environment and imperfections in the applied control fields. Here, we investigate the combination of dynamical decoupling (DD) and robust optimal control (ROC) to address this problem. In this combination, ROC is employed to find robust shaped pulses, wherein the directional derivatives of the controlled dynamics with respect to control errors are reduced to a desired order. Then, we incorporate ROC pulses into DD sequences, achieving a remarkable improvement of robustness against multiple error channels. We demonstrate this method in the example of manipulating nuclear spin bath via an electron spin in the nitrogen-vacancy center system. Simulation results indicate that ROC-based DD sequences outperform the state-of-the-art robust DD sequences. Our work has implications for robust quantum control on near-term noisy quantum devices.

Navin Khaneja