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Quantum control, which refers to the active manipulation of physical systemsdescribed by the laws of quantum mechanics, constitutes an essential ingredientfor the development of quantum technology. Here we apply DifferentiableProgramming (DP) and Natural Evolution Strategies (NES) to the optimaltransport of Majorana zero modes in superconducting nanowires, a key element tothe success of Majorana-based topological quantum computation. We formulate themotion control of Majorana zero modes as an optimization problem for which wepropose a new categorization of four different regimes with respect to thecritical velocity of the system and the total transport time. In addition tocorrectly recovering the anticipated smooth protocols in the adiabatic regime,our algorithms uncover efficient but strikingly counter-intuitive motionstrategies in the non-adiabatic regime. The emergent picture reveals a simplebut high fidelity strategy that makes use of pulse-like jumps at the beginningand the end of the protocol with a period of constant velocity in between thejumps, which we dub the jump-move-jump protocol. We provide a transparentsemi-analytical picture, which uses the sudden approximation and areformulation of the Majorana motion in a moving frame, to illuminate the keycharacteristics of the jump-move-jump control strategy. We verify that thejump-move-jump protocol remains robust against the presence of interactions ordisorder, and corroborate its high efficacy on a realistic proximity couplednanowire model. Our results demonstrate that machine learning for quantumcontrol can be applied efficiently to quantum many-body dynamical systems withperformance levels that make it relevant to the realization of large-scalequantum technology.

Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies