Almost-linear time decoding algorithm for topological codes
Nicolas Delfosse, Naomi Nickerson · Quantum · 2021
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 α ( n ) ) , where n is the number of physical qubits and α is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, α ( n ) ≤ 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.