Toward Useful Quantum Kernels

Supervised machine learning is a popular approach to the solution of many real-life problems. This approach is characterized by the use of labeled datasets to train algorithms for classifying data or predicting outcomes accurately. The question of the extent to which quantum computation can help improve existing classical supervised learning methods is the subject of intense research in the area of quantum machine learning. The debate centers on whether an advantage can be achieved already with current noisy quantum computer prototypes or it is strictly dependent on the full power of a fault-tolerant quantum computer. The current proposals can be classified into methods that can be suitably implemented on near-term quantum computers but are essentially empirical, and methods that use quantum algorithms with a provable advantage over their classical counterparts but only when implemented on the still unavailable fault-tolerant quantum computer. It turns out that, for the latter class, the benefit offered by quantum computation can be shown rigorously using quantum kernels, whereas the approach based on near-term quantum computers is very unlikely to bring any advantage if implemented in the form of hybrid algorithms that delegate the hard part (optimization) to the far more powerful classical computers