Continuous error correction for Ising anyons

Abstract

Quantum gates in topological quantum computation are performed by braiding non-Abelian anyons. These braiding processes can presumably be performed with very low error rates. However, to make a topological quantum computation architecture truly scalable, even rare errors need to be corrected. Error correction for non-Abelian anyons is complicated by the fact that it needs to be performed on a continuous basis and further errors may occur while we are correcting existing ones. Here, we provide the first study of this problem and prove its feasibility, establishing non-Abelian anyons as a viable platform for scalable quantum computation. We thereby focus on Ising anyons as the most prominent example of non-Abelian anyons and show that for these a finite error rate can indeed be corrected continuously. There is a threshold error rate pc > 0 such that for all error rates p < pc the probability of a logical error per time-step can be made exponentially small in the distance of a logical qubit.

Fault-Tolerant Quantum Error Correction for non-Abelian Anyons

“…Specific examples of error correcting schemes for Ising anyons [42], the Φ − Λ model [19] and Fibonacci anyons [43] have been investigated numerically and found to display threshold behaviours. Additionally, greedy hard-decision renormalization group decoders can error-correct any systems giving rise to anyonic excitations [44,45]. However, none of these studies have considered the case where the charge measurements are faulty, a serious complication for all the previous methods.…”

Majorana bound states in magnetic skyrmions

“…In practice, quasiparticle poisoning may also arise from the electrical driving of skyrmions. However, similar issues occur for the manipulation of MBSs in quantum wires as well [34][35][36], and in principle a continuous error correction is necessary for performing TQC [37]. References [38][39][40] discussed general approaches to optimization of TQC in the presence of quasiparticle poisoning.…”

Classical simulation of quantum error correction in a Fibonacci anyon code

“…Recent investigations have begun to explore quantum error correction for nonabelian anyon models [25][26][27][28][29]. Nonabelian anyon models are especially interesting because braiding and fusion of these anyons in general allows for the implementation of universal quantum computation.…”

“…Nonabelian anyon models are especially interesting because braiding and fusion of these anyons in general allows for the implementation of universal quantum computation. However, the initial studies of error-correction in nonabelian anyon systems have focused on specific models, such as the Ising anyons [25,29] and the so-called Φ-Λ model [26,27] that, while nonabelian, are not universal for quantum computation. The general dynamics of these particular anyon models is known to be efficiently classically simulable, a fact that was exploited to enable efficient simulation of error correction in these systems.…”