2024/11/27 by Ali Hamed Safwan, Safwan, Ali Hamed, Raditya Weda Bomantara +1
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Crystallography and Radiation Phenomena #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2411.18736
openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Majorana fermions and their generalizations to ℤn parafermions are considered promising building blocks of fault-tolerant quantum computers for their ability to encode quantum information nonlocally. In such topological quantum computers, highly robust quantum gates are obtained by braiding pairs of these quasi-particles. However, it is well-known that braiding Majorana fermions or parafermions only leads to a Clifford gate, hindering quantum universality. This paper establishes an exact mapping between Majorana fermions to ℤ4 parafermions in systems under total parity non-conserving and total parity conserving setting. It is revealed that braiding of Majorana fermions may lead to non-Clifford quantum gates in the 4-dimensional qudit representation spanned by ℤ4 parafermions, whilst braiding of ℤ4 parafermions may similarly yield non-Clifford quantum gates in the qubit representation spanned by Majorana fermions. This finding suggests that topologically protected universal quantum computing may be possible with Majorana fermions (ℤ4 parafermions) by supplementing the usual braiding operations with the braiding of ℤ4 parafermions (Majorana fermions) that could be formed out of Majorana fermions (ℤ4 parafermions) via the mapping prescribed here. Finally, the paper discusses how braiding of Majorana fermions or ℤ4 parafermions could be obtained via a series of parity measurements.