Optimisation-free Classification and Density Estimation with Quantum Circuits

TL;DR

This paper introduces a novel quantum machine learning framework for density estimation and classification that operates without circuit parameter optimization, utilizing quantum feature maps and states to summarize data distributions.

Contribution

The paper presents an optimisation-free quantum framework for classification and density estimation, with potential for quantum advantage via variational circuits.

Findings

Implemented on a real quantum device without parameter optimization.

Framework effectively summarizes data distributions using quantum states.

Discussion of variational quantum circuits for enhanced performance.

Abstract

We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a physical system through quantum feature maps. The quantum state of the arbitrarily large training data set summarises its probability distribution in a finite-dimensional quantum wave function. By projecting the quantum state of a new data sample onto the quantum state of the training data set, one can derive statistics to classify or estimate the density of the new data sample. Remarkably, the implementation of our framework on a real quantum device does not require any optimisation of quantum circuit parameters. Nonetheless, we discuss a variational quantum circuit approach that could leverage quantum advantage for our framework.