Coopmans, Luuk and Luo, Di and Kells, Graham and Clark, Bryan K. and Carrasquilla, Juan (2021) Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies. PRX Quantum, 2 (2). ISSN 2691-3399

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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 counterintuitive motion strategies in the nonadiabatic regime. The emergent picture reveals a simple but high-fidelity strategy that makes use of pulselike 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 semianalytical 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.

Item Type:	Article
Keywords:	Protocol Discovery; Quantum Control; Majoranas; Differentiable Programming; Natural Evolution Strategies;
Academic Unit:	Faculty of Science and Engineering > Theoretical Physics
Item ID:	18416
Identification Number:	https://doi.org/10.1103/PRXQuantum.2.020332
Depositing User:	Graham Kells
Date Deposited:	22 Apr 2024 14:48
Journal or Publication Title:	PRX Quantum
Publisher:	American Physical Society
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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