Multidimensional Bose quantum error correction based on neural network decoder

Abstract

Boson quantum error correction is an important means to realize quantum error correction information processing. In this paper, we consider the connection of a single-mode Gottesman-Kitaev-Preskill (GKP) code with a two-dimensional (2D) surface (surface-GKP code) on a triangular quadrilateral lattice. On the one hand, we use a Steane-type scheme with maximum likelihood estimation for surface-GKP code error correction. On the other hand, the minimum-weight perfect matching (MWPM) algorithm is used to decode surface-GKP codes. In the case where only the data GKP qubits are noisy, the threshold reaches σ ≈ 0.5 (p¯ ≈ 12.3 %). If the measurement is also noisy, the threshold is reached σ ≈ 0.25 (p¯ ≈ 10.02 %). More importantly, we introduce a neural network decoder. When the measurements in GKP error correction are noise-free, the threshold reaches σ ≈ 0.78 (p¯ ≈ 15.12 %). The threshold reaches σ ≈ 0.34 (p¯ ≈ 11.37 %) when all measurements are noisy. Through the above optimization method, multi-party quantum error correction will achieve a better guarantee effect in fault-tolerant quantum computing.