• k-means
• algorithm
• clustering
• quantum

In this thesis we face the problem of clustering with the aim of designing a
quantum version of the well-known k-means algorithm. The k-means clustering
algorithm is an unsupervised learning algorithm and its goal is to find natural groups
of elements in a data set, so that elements inside a group are more similar to each
other than elements in another group, according to a specific distance measure.
Building a quantum version of that algorithm means creating a quantum circuit
which takes classical data as input and it exploits quantum gates to perform the
computation, satisfying all the quantum mechanical constraints. The thesis provides a step by step quantization of the classical algorithm, showing advantages in terms of theoretical complexity.