Shot-frugal and Robust quantum kernel classifiers

Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and because of the constraints of near-term quantum hardware. We emphasize that for classification tasks, the aim is reliable classification and not precise kernel evaluation, and demonstrate that the former is far more resource efficient. Furthermore, it is shown that the accuracy of classification is not a suitable performance metric in the presence of noise and we motivate a new metric that characterizes the reliability of classification. We then obtain a bound for N which ensures, with high probability, that classification errors over a dataset are bounded by the margin errors of an idealized quantum kernel classifier. Using chance constraint programming and the subgaussian bounds of quantum kernel distributions, we derive several Shot-frugal and Robust (ShofaR) programs starting from the primal formulation of the Support Vector Machine. This significantly reduces the number of quantum measurements needed and is robust to noise by construction. Our strategy is applicable to uncertainty in quantum kernels arising from any source of unbiased noise.Comment: 25 pages, 8 figs, 6 table

Testing the skill of numerical hydraulic modeling to simulate spatiotemporal flooding patterns in the Logone floodplain, Cameroon

Recent innovations in hydraulic modeling have enabled global simulation of rivers, including simulation of their coupled wetlands and floodplains. Accurate simulations of floodplains using these approaches may imply tremendous advances in global hydrologic studies and in biogeochemical cycling. One such innovation is to explicitly treat sub-grid channels within two-dimensional models, given only remotely sensed data in areas with limited data availability. However, predicting inundated area in floodplains using a sub-grid model has not been rigorously validated. In this study, we applied the LISFLOOD-FP hydraulic model using a sub-grid channel parameterization to simulate inundation dynamics on the Logone River floodplain, in northern Cameroon, from 2001 to 2007. Our goal was to determine whether floodplain dynamics could be simulated with sufficient accuracy to understand human and natural contributions to current and future inundation patterns. Model inputs in this data-sparse region include in situ river discharge, satellite-derived rainfall, and the shuttle radar topography mission (SRTM) floodplain elevation. We found that the model accurately simulated total floodplain inundation, with a Pearson correlation coefficient greater than 0.9, and RMSE less than 700 km2, compared to peak inundation greater than 6000 km2. Predicted discharge downstream of the floodplain matched measurements (Nash–Sutcliffe efficiency of 0.81), and indicated that net flow from the channel to the floodplain was modeled accurately. However, the spatial pattern of inundation was not well simulated, apparently due to uncertainties in SRTM elevations. We evaluated model results at 250, 500 and 1000-m spatial resolutions, and found that results are insensitive to spatial resolution. We also compared the model output against results from a run of LISFLOOD-FP in which the sub-grid channel parameterization was disabled, finding that the sub-grid parameterization simulated more realistic dynamics. These results suggest that analysis of global inundation is feasible using a sub-grid model, but that spatial patterns at sub-kilometer resolutions still need to be adequately predicted.No Full Tex