Quantum Error Correction with Non-Abelian Topological Codes | Seminar Series with Guanyu Zhu

Speaker: Guanyu Zhu Host: Zlatko Minev, Ph.D. Title: Quantum Error Correction with Non-Abelian Topological Codes Abstract: The surface code is one of the most promising candidates to realize fault-tolerant quantum computation in the near term. However, a large overhead exists due to the need of magic state distillation. An alternative approach is resroting to non-Abelian topological codes which can perform universal quantum computing via braiding non-Abelian anyons in two spatial dimension. In this talk, we consider a two-dimensional quantum memory of qubits which realizes the non-Abelian Turaev-Viro code, and devise strategies for error correction when those qubits are subjected to depolarizing noise. Building on the concept of tube algebras from topological quantum field theory, we construct a set of measurements and of quantum gates which map arbitrary qubit errors to the string-net subspace and allow for the characterization of the resulting error syndrome in terms of doubled Fibonacci anyons. Tensor network techniques then allow to quantitatively study the action of Pauli noise on the string-net subspace. We perform Monte Carlo simulations of error correcting this Fibonacci code, and compare the performance of several decoders. For the case of a fixed-rate sampling depolarizing noise model, we find an error correction threshold of 4.7% using a clustering decoder. To the best of our knowledge, this is the first time that a threshold has been estimated for a two-dimensional error correcting code for which universal quantum computation can be performed within its code space via braiding anyons. -- The Qiskit Seminar Series is a deep dive into various academic and research topics within the quantum community. It will feature community members and leaders every Friday, 12 PM EDT.

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