Non-Abelian quantum error correction

Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strengths of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size L from to for any We apply our algorithm to decoding quantum double models and a non-Abelian anyon model with Fibonacci-like fusion rules, and show that it indeed significantly outperforms previous HDRG decoders. Furthermore, we provide the first study of continuous error correction with imperfect syndrome measurements for the quantum double models. The parallelized runtime of our algorithm is for the perfect measurement case. In the continuous case with imperfect syndrome measurements, the averaged runtime is for Abelian systems, while continuous error correction for non-Abelian anyons stays an open problem.Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strengths of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size L from to for any We apply our algorithm to decoding quantum double models and a non-Abelian anyon model with Fibonacci-like fusion rules, and show that it indeed significantly outperforms previous HDRG decoders. Furthermore, we provide the first study of continuous error correction with imperfect syndrome measurements for the quantum double models. The parallelized runtime of our algorithm is for the perfect measurement case. In the continuous case with imperfect syndrome measurements, the averaged runtime is for Abelian systems, while continuous error correction for non-Abelian anyons stays an open problem.

arXiv:1410.4478New Journal of PhysicsMar 31, 201539 citations

Realization of quantum error correction

John Chiaverini, Dietrich G. Leibfried, Tobias Schaetz +9 more

NatureDec 1, 2004517 citations

Error Correction for Quantum Computers

WORLD SCIENTIFIC eBooksJul 1, 19980 citations

Continuous error correction for Ising anyons

Adrian Hutter, James R. Wootton

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 prove the feasibility of this task, 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 ${p}_{c}>0$ such that for all error rates $p<{p}_{c}$ the probability of a logical error per time step can be made exponentially small in the distance of a logical qubit.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 prove the feasibility of this task, 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 ${p}_{c}>0$ such that for all error rates $p<{p}_{c}$ the probability of a logical error per time step can be made exponentially small in the distance of a logical qubit.

arXiv:1508.04033Physical Review AApr 18, 201611 citations

Coherent errors in quantum error correction

Daniel Greenbaum, Zachary Dutton

APSMar 1, 20172 citations

{p}_{c}>0

such that for all error rates

p<{p}_{c}

the probability of a logical error per time step can be made exponentially small in the distance of a logical qubit.