Universal quantum computing with parafermions assisted by a half fluxon

Abstract

Braiding of anyons such as Majoranas or parafermions provides only Clifford gates which do not form a universal set of quantum gates. We propose a robust and resource-efficient scheme to perform a non-Clifford gate on a logical qudit encoded in parafermionic zero modes via the Aharonov-Casher effect. This gate can be implemented by moving a half flux quantum around the pair of parafermionic zero modes. The parafermion modes can be realized in a two-dimensional set-up using existing proposals and a half fluxon carrying half flux quantum can be created as a part of a half fluxon/anti-half fluxon pair in a spin-triplet Josephson junction with a dipole defect. With an appropriate bias current pulse, the half fluxon can be braided around the parafermions. Supplementing this gate with the braiding of parafermions provides the avenue for universal quantum computing with parafermions without magic state distillation.

arXiv comment9+7 pages, 3+1 figures, longer version with appendix and more details

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Cited by in corpus (5)

• Qudits and high-dimensional quantum computing
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Topological contextuality and anyonic statistics of photonic-encoded parafermions
• Phase diagram of an extended parafermion chain