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

A Protein Phosphorylation Threshold for Functional Stacking of Plant Photosynthetic Membranes

Phosphorylation of photosystem II (PSII) proteins affects macroscopic structure of thylakoid photosynthetic membranes in chloroplasts of the model plant Arabidopsis. In this study, light-scattering spectroscopy revealed that stacking of thylakoids isolated from wild type Arabidopsis and the mutant lacking STN7 protein kinase was highly influenced by cation (Mg++) concentrations. The stacking of thylakoids from the stn8 and stn7stn8 mutants, deficient in STN8 kinase and consequently in light-dependent phosphorylation of PSII, was increased even in the absence of Mg++. Additional PSII protein phosphorylation in wild type plants exposed to high light enhanced Mg++-dependence of thylakoid stacking. Protein phosphorylation in the plant leaves was analyzed during day, night and prolonged darkness using three independent techniques: immunoblotting with anti-phosphothreonine antibodies; Diamond ProQ phosphoprotein staining; and quantitative mass spectrometry of peptides released from the thylakoid membranes by trypsin. All assays revealed dark/night-induced increase in phosphorylation of the 43 kDa chlorophyll-binding protein CP43, which compensated for decrease in phosphorylation of the other PSII proteins in wild type and stn7, but not in the stn8 and stn7stn8 mutants. Quantitative mass spectrometry determined that every PSII in wild type and stn7 contained on average 2.5±0.1 or 1.4±0.1 phosphoryl groups during day or night, correspondingly, while less than every second PSII had a phosphoryl group in stn8 and stn7stn8. It is postulated that functional cation-dependent stacking of plant thylakoid membranes requires at least one phosphoryl group per PSII, and increased phosphorylation of PSII in plants exposed to high light enhances stacking dynamics of the photosynthetic membranes

Phosphorylation of Photosystem II Controls Functional Macroscopic Folding of Photosynthetic Membranes in Arabidopsis[C][W][OA]

Photosynthetic thylakoid membranes in plants contain highly folded membrane layers enriched in photosystem II, which uses light energy to oxidize water and produce oxygen. The sunlight also causes quantitative phosphorylation of major photosystem II proteins. Analysis of the Arabidopsis thaliana stn7xstn8 double mutant deficient in thylakoid protein kinases STN7 and STN8 revealed light-independent phosphorylation of PsbH protein and greatly reduced N-terminal phosphorylation of D2 protein. The stn7xstn8 and stn8 mutants deficient in light-induced phosphorylation of photosystem II had increased thylakoid membrane folding compared with wild-type and stn7 plants. Significant enhancement in the size of stacked thylakoid membranes in stn7xstn8 and stn8 accelerated gravity-driven sedimentation of isolated thylakoids and was observed directly in plant leaves by transmission electron microscopy. Increased membrane folding, caused by the loss of light-induced protein phosphorylation, obstructed lateral migration of the photosystem II reaction center protein D1 and of processing protease FtsH between the stacked and unstacked membrane domains, suppressing turnover of damaged D1 in the leaves exposed to high light. These findings show that the high level of photosystem II phosphorylation in plants is required for adjustment of macroscopic folding of large photosynthetic membranes modulating lateral mobility of membrane proteins and sustained photosynthetic activity