Efficient control for quantum many-body systems

Quantum many-body control is among most challenging problems in the field of quantum technologies, yet it is absolutely essential for further developments of this vast field. In this work, we propose a novel approach for solving control problems of many-body quantum systems. The key feature of our approach is the ability to run tens of thousands of iterations of a gradient-based optimization of a control signal within reasonable time. This is achieved by a tensor-networks-based reduced-order modeling scheme allowing one to build a low-dimensional reduced-order model of a many-body system, whose numerical simulation in many orders of magnitude faster and more memory efficient than for the original model; these reduced-order models can be seen as "digital twins" of many-body systems. The control protocols developed for the "twins" can be directly applied to the quantum many-body system of interest. We validate the proposed method by demonstrating solutions of control problems for a one-dimensional XYZ model, such as controllable information spreading/transmission over the system, and for a spin chain in many-body localization phase, such as controllable dynamics inversion. Interestingly, our approach by design uses environmental effects (such as non-Markovianity) to make control protocols more efficient: instead of fighting against a potential loss caused by the interaction with the environment, the method uses interaction as a communication protocol with environment that is used as a "memory" for storage of quantum information.