Braiding Majorana fermions and creating quantum logic gates with vortices on a periodic pinning structure

Ma, Xia; Reichhardt, Cynthia Jane O.; Reichhardt, Charles

doi:10.1103/physrevb.101.024514

Title: Braiding Majorana fermions and creating quantum logic gates with vortices on a periodic pinning structure

Journal Article · 21 January 2020 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.101.024514 · OSTI ID:1819144

Ma, Xia ^[1];

^[2]; Reichhardt, Charles ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Notre Dame, IN (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a CNOT gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1819144

Report Number(s):: LA-UR--19-30449

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 2 Vol. 101; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Pinning and movement of individual nanoscale magnetic skyrmions via defects Hanneken, Christian; Kubetzka, André; von Bergmann, Kirsten arXiv https://doi.org/10.48550/arxiv.1601.05204	text	January 2016
Mechanical control of individual superconducting vortices Kremen, Anna; Wissberg, Shai; Haham, Noam arXiv https://doi.org/10.48550/arxiv.1602.02402	text	January 2016
Optical Manipulation of Single Flux Quanta Veshchunov, I. S.; Magrini, W.; Mironov, S. V. arXiv https://doi.org/10.48550/arxiv.1608.07453	text	January 2016
Hysteretic vortex matching effects in high-$T_c$ superconductors with nanoscale periodic pinning landscapes fabricated by He ion beam projection technique Zechner, G.; Jausner, F.; Haag, L. T. arXiv https://doi.org/10.48550/arxiv.1706.07647	text	January 2017
Fractional Josephson Vortices and Braiding of Majorana Zero Modes in Planar Superconductor-Semiconductor Heterostructures Stern, Ady; Berg, Erez arXiv https://doi.org/10.48550/arxiv.1810.01200	text	January 2018
Finite temperature effects on Majorana bound states in chiral $p$-wave superconductors Røising, Henrik Schou; Ilan, Roni; Meng, Tobias arXiv https://doi.org/10.48550/arxiv.1901.09933	text	January 2019
Manipulation of Magnetic Skyrmions by Superconducting Vortices in Ferromagnet-Superconductor Heterostructures Menezes, Raí M.; Neto, José F. S.; Silva, Clécio C. de Souza arXiv https://doi.org/10.48550/arxiv.1904.04537	text	January 2019
Manipulating multi-vortex states in superconducting structures Polshyn, Hryhoriy; Naibert, Tyler; Budakian, Raffi arXiv https://doi.org/10.48550/arxiv.1905.06303	text	January 2019
Non-abelian statistics of half-quantum vortices in p-wave superconductors Ivanov, D. A. arXiv https://doi.org/10.48550/arxiv.cond-mat/0005069	text	January 2000
Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits Georgiev, Lachezar S. arXiv https://doi.org/10.48550/arxiv.hep-th/0611340	text	January 2006
Pinning And Movement Of Individual Nanoscale Magnetic Skyrmions Via Defects Hanneken, Christian; Kubetzka, André; von Bergmann, Kirsten Zenodo https://doi.org/10.5281/zenodo.155321	dataset	January 2016
Deterministic creation and braiding of chiral edge vortices Wang, Lin; Akhmerov, A. R. Zenodo https://doi.org/10.5281/zenodo.2556946	dataset	January 2019
Deterministic creation and braiding of chiral edge vortices Wang, Lin; Akhmerov, A. R. Zenodo https://doi.org/10.5281/zenodo.2556947	dataset	January 2019
Majorana bound states in magnetic skyrmions Yang, Guang; Stano, Peter; Klinovaja, Jelena American Physical Society https://doi.org/10.5451/unibas-ep53471	text	January 2016

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