Conlon, A and Pellegrino, D. and Slingerland, Joost and Dooley, S and Kells, G. (2019) Error generation and propagation in Majorana-based topological qubits. Physical Review B, 100 (134307). ISSN 1098-0121

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Abstract

We investigate dynamical evolution of a topological memory that consists of two p-wave superconducting wires separated by a non-topological junction, focusing on the primary errors (i.e., qubit-loss) and secondary errors (bit and phase-flip) that arise due to non-adiabaticity. On the question of qubit-loss we examine the system’s response to both periodic boundary driving and deliberate shuttling of the Majorana bound states. In the former scenario we show how the frequency dependent rate of qubit-loss is strongly correlated with the local density of states at the edge of wire, a fact that can make systems with a larger gap more susceptible to high frequency noise. In the second scenario we confirm previous predictions concerning super-adiabaticity and critical velocity, but see no evidence that the coordinated movement of edge boundaries reduces qubit-loss. Our analysis on secondary bit flip errors shows that it is necessary that non-adiabaticity occurs in both wires and that inter-wire tunnelling be present for this error channel to be open. We also demonstrate how such processes can be minimised by disordering central regions of both wires. Finally we identify an error channel for phase flip errors, which can occur due to mismatches in the energies of states with bulk excitations. In the non-interacting system considered here this error systematically opposes the expected phase rotation due to finite size splitting in the qubit subspace.

Item Type:	Article
Additional Information:	This is the preprint version of the published article, which is available at Error generation and propagation in Majorana-based topological qubits A. Conlon, D. Pellegrino, J. K. Slingerland, S. Dooley, and G. Kells Phys. Rev. B 100, 134307 – Published 15 October 2019. DOI:https://doi.org/10.1103/PhysRevB.100.134307. The arXiv preprint is available at arXiv:1905.06923
Keywords:	error generation; propagation; Majorana; based; topological qubits;
Academic Unit:	Faculty of Science and Engineering > Theoretical Physics
Item ID:	13885
Identification Number:	https://doi.org/10.1103/PhysRevB.100.134307
Depositing User:	Dr. Joost Slingerland
Date Deposited:	01 Feb 2021 12:09
Journal or Publication Title:	Physical Review B
Publisher:	American Physical Society
Refereed:	Yes
URI:	Publisher Organisation
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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