  Quantum computing leverages quantum effects to build algorithms that are
faster then their classical variants. In machine learning, for a given model
architecture, the speed of training the model is typically determined by the
size of the training dataset. Thus, quantum machine learning methods have the
potential to facilitate learning using extremely large datasets. While the
availability of data for training machine learning models is steadily
increasing, oftentimes it is much easier to collect feature vectors that to
obtain the corresponding labels. One of the approaches for addressing this
issue is to use semi-supervised learning, which leverages not only the labeled
samples, but also unlabeled feature vectors. Here, we present a quantum machine
learning algorithm for training Semi-Supervised Kernel Support Vector Machines.
The algorithm uses recent advances in quantum sample-based Hamiltonian
simulation to extend the existing Quantum LS-SVM algorithm to handle the
semi-supervised term in the loss. Through a theoretical study of the
algorithm's computational complexity, we show that it maintains the same
speedup as the fully-supervised Quantum LS-SVM.
