  Quantum machine learning with quantum kernels for classification problems is
a growing area of research. Recently, quantum kernel alignment techniques that
parameterise the kernel have been developed, allowing the kernel to be trained
and therefore aligned with a specific dataset. While quantum kernel alignment
is a promising technique, it has been hampered by considerable training costs
because the full kernel matrix must be constructed at every training iteration.
Addressing this challenge, we introduce a novel method that seeks to balance
efficiency and performance. We present a sub-sampling training approach that
uses a subset of the kernel matrix at each training step, thereby reducing the
overall computational cost of the training. In this work, we apply the
sub-sampling method to synthetic datasets and a real-world breast cancer
dataset and demonstrate considerable reductions in the number of circuits
required to train the quantum kernel while maintaining classification accuracy.
