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We discuss the feasibility of measurement-based braiding in semiconductor-superconductor (SM-SC) heterostructures in the so-called quasi-Majorana regime—the topologically-trivial regime characterized by robust zero-bias conductance peaks (ZBCPs) that are due to partially-separated Andreev bound states (ps-ABSs). These low energy ABSs consist of component Majorana bound states (also called quasi-Majorana modes) that are spatially separated by a length scale smaller than the length of the system, in contrast with the Majorana zero modes (MZMs) emerging in the topological regime, which are separated by the length of the wire. In the quasi-Majorana regime, the ZBCPs appear to be robust to various perturbations as long as the energy splitting of the ps-ABS is less than the typical width Ew of the low-energy conductance peaks (Ew ∼ 10–20 μeV). However, the feasibility of measurement-based braiding depends on a different, much smaller, energy scale Em ∼ 0.1 μeV. This energy scale is given by the typical fermion parity-dependent ground state energy shift due to virtual electron transfer between the SM-SC system and a quantum dot used for parity measurements. In this paper we show that it is possible to prepare the SM-SC system in the quasi-Majorana regime with energy splittings below the Em threshold, so that measurement-based braiding is possible in principle. However, despite the apparent robustness of the corresponding ZBCPs, ps-ABSs are in reality topologically unprotected. Starting with ps-ABSs with energy below Em, we identify the maximum amplitudes of different types of (local) perturbations that are consistent with perturbation-induced energy splittings not exceeding the Em limit.We argue that measurements generating perturbations larger than the threshold amplitudes appropriate for Em cannot realize measurement-based braiding in SM-SC heterostructures in the quasi-Majorana regime. We find that, if possible at all, quantum computation using measurement-based braiding in the quasi-Majorana regime would be plagued with errors introduced by the measurement processes themselves, while such errors are significantly less likely in a scheme involving topological MZMs.
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Symmetry-protected gates of Majorana qubits in a high-$T_c$ higher-order topological superconductor platform
We propose a platform for braiding Majorana non-Abelian anyons basedon a heterostructure between a d d -wavehigh- T_c T c superconductor and a quantum spin-Hall insulator. It has been recentlyshown that such a setup for a quantum spin-Hall insulator leads to apair of Majorana zero modes at each corner of the sample, and thus canbe regarded as a higher-order topological superconductor. We show thatupon applying a Zeeman field in the region, these Majorana modes splitin space and can be manipulated for braiding processes by tuning thefield and pairing phase. We show that such a setup can achieve fullbraiding, exchanging, and arbitrary phase gates (including the \pi/8 π / 8 magic gates) of the Majorana zero modes, all of which are robust andprotected by symmetries. As many of the ingredients of our proposedplatform have been realized in recent experiments, our results provide anew route toward universal topological quantum computation.
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- PAR ID:
- 10320820
- Date Published:
- Journal Name:
- SciPost Physics
- Volume:
- 11
- Issue:
- 5
- ISSN:
- 2542-4653
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.21468/SciPostPhys.11.5.086
