  Quantum control, which refers to the active manipulation of physical systems
described by the laws of quantum mechanics, constitutes an essential ingredient
for the development of quantum technology. Here we apply Differentiable
Programming (DP) and Natural Evolution Strategies (NES) to the optimal
transport of Majorana zero modes in superconducting nanowires, a key element to
the success of Majorana-based topological quantum computation. We formulate the
motion control of Majorana zero modes as an optimization problem for which we
propose a new categorization of four different regimes with respect to the
critical velocity of the system and the total transport time. In addition to
correctly recovering the anticipated smooth protocols in the adiabatic regime,
our algorithms uncover efficient but strikingly counter-intuitive motion
strategies in the non-adiabatic regime. The emergent picture reveals a simple
but high fidelity strategy that makes use of pulse-like jumps at the beginning
and the end of the protocol with a period of constant velocity in between the
jumps, which we dub the jump-move-jump protocol. We provide a transparent
semi-analytical picture, which uses the sudden approximation and a
reformulation of the Majorana motion in a moving frame, to illuminate the key
characteristics of the jump-move-jump control strategy. We verify that the
jump-move-jump protocol remains robust against the presence of interactions or
disorder, and corroborate its high efficacy on a realistic proximity coupled
nanowire model. Our results demonstrate that machine learning for quantum
control can be applied efficiently to quantum many-body dynamical systems with
performance levels that make it relevant to the realization of large-scale
quantum technology.
