Data-driven decoding of the surface code using a neural matching decoder

Examensarbete för masterexamen
Master's Thesis
Complex adaptive systems (MPCAS), MSc
Fjelddahl, Frida
Bengtsson, Isak
Quantum error correction is a prerequisite to achieve fault-tolerant quantum computation with noisy qubits. A promising approach is the surface code, in which the qubits have nearest-neighbour connectivity and are arranged on a two-dimensional grid. Concurrent stabilizer measurements across the grid project the qubits to a two-dimensional code space, encoding a single logical qubit. Subsequent stabilizer measurements detect if the logical qubit leaves the code space, but the measurements must be interpreted by a quantum error correction decoder to find what the actual errors are. Decoding the surface code is computationally intensive, and the decoder must be both fast and accurate if quantum error correction is to work. In this thesis, we present the novel neural matching decoder (NMD). Our decoder combines a graph neural network (GNN) with a more traditional choice, a minimum-weight perfect matching (MWPM) algorithm. Our approach is purely data-driven and does not require any prior information about the noise processes in the quantum circuits, instead the NMD is trained on 109 simulated error syndromes. This stands in contrast to conventional decoders, that require detailed noise models to achieve high decoding accuracies. Given a surface code of size d = 5 influenced by circuit-level noise for dt = 5 time steps, we show that the NMD can reach relatively high accuracies and approaches the results of a conventional MWPM decoder. This indicates that the NMD can learn the underlying noise model directly from a distribution of error syndromes. It also shows that it is possible to create a decoder by combining neural networks with a conventional algorithm. This is interesting from a computational perspective, as it could help limit the computational resources needed by the decoder whilst retaining a high accuracy. Our work opens up a new direction in the field of quantum error correction decoders, by combining machine learning with a graph algorithm. .
quantum error correction , surface code , MWPM , graph neural networks , GNN
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