Parafermions in a Kagome lattice of qubits for topological quantum computation

Abstract

Engineering complex non-Abelian anyon models with simple physical systems is crucial for topological quantum computation. Unfortunately, the simplest systems are typically restricted to Majorana zero modes (Ising anyons). Here we go beyond this barrier, showing that the ${\mathbb{Z}}_4$ parafermion model of non-Abelian anyons can be realized on a qubit lattice. Our system additionally contains the Abelian $D({\mathbb{Z}}_4)$ anyons as low-energetic excitations. We show that braiding of these parafermions with each other and with the $D({\mathbb{Z}}_4)$ anyons allows the entire $d=4$ Clifford group to be generated. The error correction problem for our model is also studied in detail, guaranteeing fault-tolerance of the topological operations. Crucially, since the non-Abelian anyons are engineered through defect lines rather than as excitations, non-Abelian error correction is not required. Instead the error correction problem is performed on the underlying Abelian model, allowing high noise thresholds to be realized.

11+10 pages, 14 figures; v2: accepted for publication in Phys. Rev. X; 4 new figures, performance of phase-gate explained in more detail

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Cited by in corpus (16)

• Majorana braiding with thermal noise
• Quantum Computing with Parafermions
• Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
• Transversal Clifford gates on folded surface codes
• Fermionized parafermions and symmetry-enriched Majorana modes
• Monte Carlo studies of the properties of the Majorana quantum error correction code: is self-correction possible during braiding?
• Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model
• Fault-tolerant fermionic quantum computation based on color code
• Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model
• Measurement-only topological quantum computation without forced measurements
• A Hierarchy of Anyon Models Realised by Twists in Stacked Surface Codes
• Magnetic properties and field-induced phenomena in the Jeff = 1/2 distorted kagome antiferromagnet
• Spin-charge Kondo effect for a quantum dot with side coupled Majorana zero mode
• Quantum computation with hybrid parafermion-spin qubits
• Parafermionic representation of Potts-based cluster chain
• Noninteracting tight-binding models for Fock parafermions