  Two novel measurement-based, quantum clustering algorithms are proposed based
on quantum parallelism and entanglement. The first algorithm follows a divisive
approach. The second algorithm is based on unsharp measurements, where we
construct an effect operator with a Gaussian probability distribution to
cluster similar data points. A major advantage of both algorithms is that they
are simplistic in nature, easy to implement, and well suited for noisy
intermediate scale quantum computers. We have successfully applied the first
algorithm on a concentric circle data set, where the classical clustering
approach fails, as well as on the Churrtiz data set of $130$ cities, where we
show that the algorithm succeeds with very low quantum resources. We applied
the second algorithm on the labeled Wisconsin breast cancer dataset, and found
that it is able to classify the dataset with high accuracy using only
$O(log(D))$ qubits and polynomial measurements, where $D$ is the maximal
distance within any two points in the dataset. We also show that this algorithm
works better with an assumed measurement error in the quantum system, making it
extremely well-suited for NISQ devices.
