Quantum embeddings for machine learning

TL;DR

This paper introduces quantum metric learning, training quantum embeddings to maximize class separation in Hilbert space, simplifying quantum classifiers and enhancing their efficiency for near-term quantum devices.

Contribution

It proposes a novel training strategy for quantum embeddings that improves data separation and reduces measurement complexity in quantum classifiers.

Findings

Quantum metric learning enhances class separation in Hilbert space.

The approach simplifies measurement requirements in quantum classifiers.

It provides an analytic framework for quantum machine learning.

Abstract

Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional Hilbert space; the second part of the circuit executes a quantum measurement interpreted as the output of the model. Usually, the measurement is trained to distinguish quantum-embedded data. We propose to instead train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space, a strategy we call quantum metric learning. As a result, the measurement minimizing a linear classification loss is already known and depends on the metric used: for embeddings separating data using the l1 or trace distance, this is the Helstrom measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple overlap measurement. This approach provides a powerful analytic framework for quantum machine learning and eliminates a major component in current models, freeing up more precious resources to best leverage the capabilities of near-term quantum information processors.