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 $p_c>0$ 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.

8 pages, 2 figures; v2: published version

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• Universal Quantum Computation with Hybrid Spin-Majorana Qubits
• Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
• Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment
• Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code
• Topological quantum error correction in the Kitaev honeycomb model
• A Universal Circuit Set Using the $S_3$ Quantum Double
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Universal fault tolerant quantum computation in 2D without getting tied in knots