Designer non-Abelian anyon platforms: from Majorana to Fibonacci

Abstract

The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has evolved from a highly theoretical subject to an active experimental area, particularly following proposals for trapping non-Abelian anyons in `engineered' structures built from well-understood components. In this short overview we briefly tour the impressive progress that has taken place in the quest for the simplest type of non-Abelian anyon---defects binding Majorana zero modes---and then turn to similar strategies for pursuing more exotic excitations. Specifically, we describe how interfacing simple quantum Hall systems with conventional superconductors yields `parafermionic' generalizations of Majorana modes and even Fibonacci anyons---the latter enabling fully fault tolerant universal quantum computation. We structure our treatment in a manner that unifies these topics in a coherent way. The ideas synthesized here spotlight largely uncharted experimental territory in the field of quantum Hall physics that appears ripe for discovery.

10 pages, 4 figures; lighthearted overview for proceedings of Nobel symposium on "New forms of matter: topological insulators and superconductors"

References in corpus (40)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Anyons and the quantum Hall effect - a pedagogical review
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Induced Superconductivity in the Quantum Spin Hall Edge
• Measurement-Only Topological Quantum Computation
• Genons, twist defects, and projective non-Abelian braiding statistics
• Edge-mode Superconductivity in a Two Dimensional Topological Insulator
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Braiding statistics of loop excitations in three dimensions
• Fractional topological superconductors with fractionalized Majorana fermions
• Time-Reversal Invariant Parafermions in Interacting Rashba Nanowires
• Momentum space imaging of Cooper pairing in a half-Dirac-gas topological superconductor (a helical 2D topological superconductor)
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states
• Parafermions in Interacting Nanowire Bundle
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Stability of zero modes in parafermion chains
• Exotic circuit elements from zero-modes in hybrid superconductor/quantum Hall systems
• Layer construction of 3D topological states and string braiding statistics
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Self-organized topological state in the magnetic chain on the surface of a superconductor
• Parafermionic conformal field theory on the lattice
• Measurement-Only Topological Quantum Computation via Tunable Interactions
• Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations
• Criticality in Translation-Invariant Parafermion Chains
• Generalized Kitaev Models and Slave Genons
• Experimental Proposal to Detect Topological Ground State Degeneracy
• Z${}_N$ parafermion zero modes without Fractional Quantum Hall effect

Cited by in corpus (22)

• High-Temperature Majorana Corner States
• Introduction to topological quantum computation with non-Abelian anyons
• Majorana nanowires for topological quantum computation
• Majorana bound states in semiconducting nanostructures
• Evidence for chiral supercurrent in quantum Hall Josephson junctions
• Majoranas in Noisy Kitaev Wires
• Parafermionic clock models and quantum resonance
• Ballistic Josephson junctions in the presence of generic spin dependent fields
• Measurement and control of a Coulomb-blockaded parafermion box
• Parafermionic generalization of the topological Kondo effect
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Topological superconductivity in Landau levels
• Phase diagram of superconductivity in the integer quantum Hall regime
• Universal quantum computing with parafermions assisted by a half fluxon
• Low-temperature environments for quantum computation and quantum simulation
• Fractional Josephson effect in nonuniformly strained graphene
• Bulk Pumping in 2D Topological Phases
• Quantum Hall valley Ferromagnets as a platform for topologically protected quantum memory
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators
• Spin-charge Kondo effect for a quantum dot with side coupled Majorana zero mode
• Quantum computation with hybrid parafermion-spin qubits