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

• URL: http://arxiv.org/abs/2008.09128v2
• Date: Fri, 9 Apr 2021 12:54:17 GMT
• Title: Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• Authors: Luuk Coopmans, Di Luo, Graham Kells, Bryan K. Clark and Juan Carrasquilla
• Abstract summary: We applyDP andNES to the optimal transport of Majorana zero modes in superconducting nanowires. We identify efficient but strikingly counter-intuitive motion strategies in the non-adiabatic regime. Our results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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