  Quantum algorithms can enhance machine learning in different aspects. Here,
we study quantum-enhanced least-square support vector machine (LS-SVM).
Firstly, a novel quantum algorithm that uses continuous variable to assist
matrix inversion is introduced to simplify the algorithm for quantum LS-SVM,
while retaining exponential speed-up. Secondly, we propose a hybrid
quantum-classical version for sparse solutions of LS-SVM. By encoding a large
dataset into a quantum state, a much smaller transformed dataset can be
extracted using quantum matrix toolbox, which is further processed in classical
SVM. We also incorporate kernel methods into the above quantum algorithms,
which uses both exponential growth Hilbert space of qubits and infinite
dimensionality of continuous variable for quantum feature maps. The quantum
LS-SVM exploits quantum properties to explore important themes for SVM such as
sparsity and kernel methods, and stresses its quantum advantages ranging from
speed-up to the potential capacity to solve classically difficult machine
learning tasks.
