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.
Highlights
Non-Abelian anyons exhibit exotic physics that would make them an ideal basis for topological quantum computation [1,2,3]
It has recently become apparent that truly scalable quantum computation with non-Abelian anyons can only be achieved when invoking active error correction, despite the protection provided by a finite anyon gap [4,5,6]
Systems in which nonAbelian anyons arise typically suffer from one of two drawbacks: Either they are experimentally extremely challenging to realize, or it is not clear how they can be made compatible with the active error correction required for fault tolerance
Summary
Non-Abelian anyons exhibit exotic physics that would make them an ideal basis for topological quantum computation [1,2,3]. A variety of proposals for experimental realization of Majorana zero modes in solid-state systems have been developed [16] These anyons can be used to perform universal quantum computation when enhanced by nontopological operations [17,18]. Abelian excitations of the quantum double model, allowing us to generate the entire Clifford group for d 1⁄4 4 by quasiparticle braiding. This extends beyond the limited set of gates found using the same parafermions in previous work [21]. We label the vertices around one triangle a, b, and c, and the two qubits that are present
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