Unsupervised clustering in quantum feature spaces using quantum similarity matrices

Abstract

A method of performing unsupervised clustering of data points includes determining a number of qubits to include in a quantum processor based on feature dimensions of each data point. The method includes, for each pair of data points, executing a quantum circuit on a quantum processor having the determined number of qubits. The quantum circuit includes a feature map template circuit parameterized with a first plurality of rotations, a backward feature map template circuit parameterized with a second plurality of rotations, and a measurement circuit that outputs a similarity measure. The method includes creating a similarity matrix based on the similarity measure for each pair of data points, and inputting the similarity matrix to a classical clustering algorithm to cluster the data points. The feature map template circuit and the backward feature map template circuit each use quantum properties of superposition and entanglement of the qubits of the quantum processor.