  Current quantum hardware prohibits any direct use of large classical
datasets. Coresets allow for a succinct description of these large datasets and
their solution in a computational task is competitive with the solution on the
original dataset. The method of combining coresets with small quantum computers
to solve a given task that requires a large number of data points was first
introduced by Harrow [arXiv:2004.00026]. In this paper, we apply the coreset
method in three different well-studied classical machine learning problems,
namely Divisive Clustering, 3-means Clustering, and Gaussian Mixture Model
Clustering. We provide a Hamiltonian formulation of the aforementioned problems
for which the number of qubits scales linearly with the size of the coreset.
Then, we evaluate how the variational quantum eigensolver (VQE) performs on
these problems and demonstrate the practical efficiency of coresets when used
along with a small quantum computer. We perform noiseless simulations on
instances of sizes up to 25 qubits on CUDA Quantum and show that our approach
provides comparable performance to classical solvers.
