Optimal control simulations of many-body quantum systems by synergism of discrete real-time learning and quantum optimal control theory

A high-fidelity and low-cost quantum control algorithm that can be applied to a wide range of many-body quantum systems is essential to the understanding of many-body quantum control as well as for advancements in quantum technology. Existing many-body quantum control methods often utilize the tensor network-based density matrix renormalization group (DMRG) method, which is generally only applicable to one-dimensional (1D) systems. This presentation will introduce a self-consistent algorithm for optimal control simulations of many-body quantum systems. The algorithm features a two-step synergism of the recently developed discrete real-time learning (DRTL) method for training variational many-body neural-network quantum states combined with Quantum Optimal Control Theory (QOCT) using the time-dependent Schrödinger equation. We demonstrate the high efficiency and fidelity of this two-step self-consistent DRTL-QOCT method by considering the optimal control simulations of the time evolution of strongly interacting 1D and 2D Heisenberg spin systems under the local control condition that only a single spin is driven by the time-dependent control fields. It is found that the method can identify reduced-dimensional Hilbert spaces for the desired optimally controlled dynamics with just a few iterations. In particular, the dimensionality of the latter reduced spaces scales only quasi-linearly with the number of spins.