Quantum-Inspired Classification Based on Voronoi Tessellation and Pretty-Good Measurements

Abstract

In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination.

Local Approach to Quantum-inspired Classification

“…In quantum-inspired machine learning, the encoding of data instances into Bloch vectors of density operators turns out to be a useful geometric tool to reduce memory consumption in defining feature maps into higher dimensional spaces [4]. Let us consider the simplest case of encoding data vectors in R 2 to density operators on C 2 by means of the Bloch representation of qubit states:…”

“…In the experimental part, we present a comparison of the performances of the local quantuminspired classifiers against well-known classical algorithms in order to show that the local approach can be a valuable tool for increasing the performances of this kind of classifiers. A seminal research on a particular local approach based on the Voronoi tessellation of the training set to a quantum-inspired classifier defined by PGM is presented in [4].…”