Almostlinear time decoding algorithm for topological codes
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 $(d1)/2$ and for loss of up to $d1$ qubits, where $d$ is the minimum distance of the code. Numerically, we obtain a threshold of $9.9\%$ for the 2dtoric code with perfect syndrome measurements and $2.6\%$ with faulty measurements.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 DOI:
 10.48550/arXiv.1709.06218
 arXiv:
 arXiv:1709.06218
 Bibcode:
 2017arXiv170906218D
 Keywords:

 Quantum Physics
 EPrint:
 Quantum 5, 595 (2021)