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 superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge- 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 twofold ground-state degeneracy on a torus. In contrast to a superconductor, vortices do not yield additional particle types, yet depending on nonuniversal 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.
3 More- Received 2 August 2013
DOI:https://doi.org/10.1103/PhysRevX.4.011036
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Published by the American Physical Society
Popular Summary
The concept of a quantum computer promises great technological advances in areas ranging from cryptography to quantum simulation and beyond. Its realization, however, poses a grand challenge for physics. One of the fundamental obstacles is “decoherence”—the easy corruption of quantum information by environmental perturbations. The paradigm of “topological” quantum computation cleverly sidesteps decoherence at the hardware level by using emergent exotic particles known as non-Abelian anyons as noise-resistant carriers of quantum information. This paradigm nevertheless comes with its own price, as non-Abelian anyons are not easily found experimentally. A natural question therefore arises: Can one engineer a fully fault-tolerant, universal quantum computer based on non-Abelian anyons by judiciously combining well-understood materials? In this paper, we answer this question in the affirmative with a concrete design principle.
The fundamental insight underlying our design is that we can emulate the physics of highly exotic non-Abelian quantum Hall systems—where non-Abelian anyons can emerge—by combining simple fractional quantum Hall states with conventional superconductors. Most interestingly, we have proposed and theoretically demonstrated that a heterostructure made of these two types of systems supports so-called Fibonacci anyons. These particles constitute the “holy grail” for topological quantum computing in that they allow for computational universality via a single elementary logical gate generated by “braiding” the anyons around each other.
Our results suggest a promising new avenue towards scalable quantum computation and also reveal deep links between topics in statistical mechanics, field theory, quantum Hall physics, and superconductivity.