Data-driven decoding of the surface code using a neural matching decoder
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Complex adaptive systems (MPCAS), MSc
Publicerad
2024
Författare
Fjelddahl, Frida
Bengtsson, Isak
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
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Beskrivning
Ämne/nyckelord
quantum error correction , surface code , MWPM , graph neural networks , GNN