Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure

TL;DR

This paper proposes a method to realize universal topological quantum computation by engineering a superconductor/Abelian quantum Hall heterostructure that supports Fibonacci anyons, enabling braiding-based quantum computing.

Contribution

It establishes a novel correspondence between the Z_3 Read-Rezayi quantum Hall state and a new superconductor supporting Fibonacci anyons for universal quantum computation.

Findings

Fibonacci anyons can be realized in superconductor/quantum Hall heterostructures.

Vortices can serve as traps for Fibonacci anyons depending on energetics.

The proposed blueprint uses Abelian quantum Hall states with superconducting islands.

Abstract

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z_3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that---unlike Ising anyons---allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a two-fold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types yet depending on non-universal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.