Measurement and control of a Coulomb-blockaded parafermion box

Abstract

Parafermionic zero modes are fractional topologically protected quasiparticles expected to arise in various platforms. We show that Coulomb charging effects define a parafermion box with unique access options via fractional edge states and/or quantum antidots. Basic protocols for the detection, manipulation, and control of parafermionic quantum states are formulated. With those tools, one may directly observe the dimension of the zero-mode Hilbert space, prove the degeneracy of this space, and perform on-demand digital operations satisfying a parafermionic algebra.

14 pages, 5 figures, supplemental material included as a PDF printout

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Cited by in corpus (15)

• Evidence for chiral supercurrent in quantum Hall Josephson junctions
• Superconductivity and fermionic dissipation in quantum Hall edges
• Parafermion braiding in fractional quantum Hall edge states with finite chemical potential
• Number conserving analysis of measurement-based braiding with Majorana zero modes
• Parafermionic generalization of the topological Kondo effect
• Readout of parafermionic states by transport measurements
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Universal quantum computing with parafermions assisted by a half fluxon
• Quantum transport in coupled Majorana box systems
• Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes
• Quantum dots as parafermion detectors
• Dynamics of parafermionic states in transport measurements
• Manifestation of edge-bulk incompatibility in fractional quantum Hall platform
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
• Can Majorana zero modes in quantum Hall edges survive edge reconstruction?