Data-driven decoding of quantum error correcting codes using graph neural networks

To leverage the full potential of quantum error-correcting stabilizer codes it is crucial to have an efficient and accurate decoder. Accurate, maximum likelihood, decoders are computationally very expensive whereas decoders based on more efficient algorithms give sub-optimal performance. In addition, the accuracy will depend on the quality of models and estimates of error rates for idling qubits, gates, measurements, and resets, and will typically assume symmetric error channels. In this work, instead, we explore a model-free, data-driven, approach to decoding, using a graph neural network (GNN). The decoding problem is formulated as a graph classification task in which a set of stabilizer measurements is mapped to an annotated detector graph for which the neural network predicts the most likely logical error class. We show that the GNN-based decoder can outperform a matching decoder for circuit level noise on the surface code given only simulated experimental data, even if the matching decoder is given full information of the underlying error model. Although training is computationally demanding, inference is fast and scales approximately linearly with the space-time volume of the code. We also find that we can use large, but more limited, datasets of real experimental data [Google Quantum AI, Nature {\bf 614}, 676 (2023)] for the repetition code, giving decoding accuracies that are on par with minimum weight perfect matching. The results show that a purely data-driven approach to decoding may be a viable future option for practical quantum error correction, which is competitive in terms of speed, accuracy, and versatility.Comment: 15 pages, 12 figure

Karaktärisering av CEPA, en phoswich uppsättning

The structure of unstable nuclei is studied at the international facility FAIR, Darmstadt, Germany. One experimental setup at FAIR is called R3B where radioactive beams at relativistic energies impinge on a specific target which allows to collect data on the reactions taking place. For these experiments, different detectors have been built and CEPA is one of them. CEPA is the detector that will be characterized in this thesis. This detector consists of 24 sectors, where each sector has four tightly packed scintillator detectors, each a combination of LaBr3 and LaCl3, making up a phoswich crystal unit. Each phoswich crystal unit is made out of 7 cm LaBr3 and 8 cm LaCl3, respectively. Previous CEPA prototypes have been characterized at Chalmers, but the latest CEPA crystals have a new geometrical shape, the shape of a frustum. The three characteristics of CEPA that are investigated are their energy calibration, their energy resolution and the dependence of the detected energy on the position of the interaction. It was found that the energy resolution for the four LaBr3 parts of the tested sector did not meet the requirements [5]. Crystal one was the closest to meet the requirements, but still did not met the requirements with a factor 1.73 times higher (resolution) compared with the prototype, the other crystals were approximately a factor 2.5 higher. On the LaCl3 part none of the crystals met the requirements. The calibration measurements were also not successful since the characterized peak positions for different -sources did not end up on the expected place for all the sources. Unfortunately the sector that was investigated exhibited a significant position dependence