Increasing the probability of quantum tunneling between two states, while keeping constant the resources of the underlying physical system, is a task of key importance in several physical contexts and platforms, including ultracold atoms confined by double-well potentials and superconducting qubits. We propose a novel ancillary assisted protocol showing that when a quantum system—such as a qubit—is coupled to an ancilla, one can learn the optimal ancillary component and its coupling, to increase the tunneling probability. As a case study, we consider a quantum system that, due to the presence of an energy detuning between two modes, cannot transfer by tunneling the particles from one mode to the other. However, it does it through a learned coupling with an ancillary system characterized by a detuning not smaller than the one of the primary system. We provide several illustrative examples for the paradigmatic case of a two-mode system and a two-mode ancilla in the presence of interacting particles. This reduces to a qubit coupled to an ancillary qubit in the case of one particle in the system and one in the ancilla. Our proposal provides an effective method to increase the tunneling probability in all those physical situations where no direct improvement of the system parameters, such as tunneling coefficient or energy detuning, is either possible or resource efficient. Finally, we also argue that the proposed strategy is not hampered by weak coupling to noisy environments.
