Abastract:
Recently a lot of attention has been given to the prospects of realising a topological qubit based on Majorana Zero Modes. In relation to this, I will critically examine the so-called topological gap protocol (TGP). I will demonstrate that the TGP is not a reliable diagnostic tool for the presence of topological superconductivity and associated Majorana Zero Modes. Moreover, I will show that this protocol is also an unreliable method to detect a superconducting gap, a prerequisite for readout of a well-defined parity in a superconductor and the proposed basis of a putative topological qubit. Based on these insights, I will show that any kind of topological qubit is not possible in the near term, bringing into question recent announcements purporting to have achieved this.
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[2] Hess, Legg, Loss, Klinovaja Phys. Rev. Lett. 130, 207001 (2023)
[3] Legg, arXiv:2502.19560
[4] Legg, arXiv:2503.08944
[5] Nature 639, 555-556 (2025)
