1IQIM, California Institute of Technology, Pasadena, CA, USA
2Department of Physics and Astronomy, University of California, Riverside, CA, USA
3Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA
4Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
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Abstract
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of $O(n alpha(n))$, where $n$ is the number of physical qubits and $alpha$ is the inverse of Ackermann’s function, which is very slowly growing. For all practical purposes, $alpha(n) leq 3$. We prove that our algorithm performs optimally for errors of weight up to $(d-1)/2$ and for loss of up to $d-1$ qubits, where $d$ is the minimum distance of the code. Numerically, we obtain a threshold of $9.9%$ for the 2d-toric code with perfect syndrome measurements and $2.6%$ with faulty measurements.
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The above citations are from SAO/NASA ADS (last updated successfully 2021-12-02 16:04:17). The list may be incomplete as not all publishers provide suitable and complete citation data.
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Source: https://quantum-journal.org/papers/q-2021-12-02-595/
