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Adiabatic non-Abelian braiding of imperfect Majorana bound states

Maximilian Nitsch1, Viktor Svensson2, William Samuelson1, Konstantin Nestmann1, Jeroen Danon3, Karsten Flensberg4, Rubén Seoane Souto5,6, and Martin Leijnse1

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Phys. Rev. B 113, L201408 – Published 21 May, 2026

DOI: https://doi.org/10.1103/3vcb-pxp6

Abstract

Demonstration of a nontrivial result of quasiparticle exchange (or braiding) is usually considered the definitive proof of a topological phase with non-Abelian excitations, such as Majorana bound states (MBSs). However, in finite systems with disorder and smooth potential variations, the MBSs are imperfect in the sense that they are not fully isolated in space and can, to a varying degree, resemble conventional fermions. The main goal of this work is to reveal the braiding properties of isolated MBSs, regular fermions, and anything in between. We start from an experimentally attractive braiding protocol and find a way to compensate for the undesired splitting of the ground-state degeneracy which occurs during the protocol for imperfect MBSs. This leads to a braiding outcome that depends on the degree of MBS isolation but remains robust and non-Abelian except in the perfect fermion limit. Our protocol could be implemented in different platforms with non-Abelian excitations, including quantum-dot-based minimal Kitaev chains.

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Phys. Rev. B 113, L201408– Published 21 May, 2026
  • Received 15 July 2025
  • Revised 25 February 2026
  • Accepted 3 March 2026
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