Shot-frugal and Robust quantum kernel classifiers

TL;DR

This paper introduces a resource-efficient quantum kernel classification method that reduces measurement requirements and enhances robustness to noise, making quantum machine learning more practical for near-term hardware.

Contribution

It proposes Shot-frugal and Robust (ShofaR) programs that minimize quantum measurements and ensure reliable classification despite noise, advancing quantum kernel methods.

Findings

Reduces quantum measurement count for classification tasks.

Provides a noise-robust classification framework.

Establishes bounds ensuring high-probability classification accuracy.

Abstract

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.