Shot-frugal and Robust quantum kernel classifiers
This work addresses resource constraints in near-term quantum hardware for machine learning, offering a practical solution for quantum kernel classifiers, though it is incremental in improving efficiency and robustness.
The authors tackled the problem of reducing the number of quantum measurements required for reliable classification in quantum kernel methods, showing that classification can be achieved with far fewer resources than precise kernel evaluation and deriving bounds that ensure high-probability error control.
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.