Renormalization Group Decoder for a Four-Dimensional Toric Code
N.P. Breuckmann (RWTH Aachen University, University College London)
B.M. Terhal (TU Delft - Quantum Computing, TU Delft - QuTech Advanced Research Centre, Forschungszentrum Jülich)
K. Duivenvoorden (RWTH Aachen University)
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Abstract
We describe a computationally efficient heuristic algorithm based on a renormalization-group procedure which aims at solving the problem of finding a minimal surface given its boundary (curve) in any hypercubic lattice of dimension D > 2. We use this algorithm to correct errors occurring in a four-dimensional variant of the toric code, having open as opposed to periodic boundaries. For a phenomenological error model which includes measurement errors we use a five-dimensional version of our algorithm, achieving a threshold of 4.35±0.1%. For this error model, this is the highest known threshold of any topological code. Without measurement errors, a four-dimensional version of our algorithm can be used and we find a threshold of 7.3±0.1%. For the gate-based depolarizing error model we find a threshold of 0.31±0.01% which is below the threshold found for the twodimensional toric code.