A Unified Framework for Quantum Supervised Learning

TL;DR

This paper introduces a unified, embedding-based framework for quantum supervised learning that leverages trainable quantum circuits, enabling high-capacity classification and demonstrating advantages in noisy and real-device scenarios.

Contribution

It presents a novel unified framework combining explicit and implicit quantum feature mapping approaches, extending the capacity of quantum supervised learning beyond previous models.

Findings

Implicit approach allows classification of many classes with few qubits.

Framework performs well in noisy simulations and on IBM Q devices.

Unified approach connects and generalizes existing quantum supervised learning models.

Abstract

Quantum machine learning is an emerging field that combines machine learning with advances in quantum technologies. Many works have suggested great possibilities of using near-term quantum hardware in supervised learning. Motivated by these developments, we present an embedding-based framework for supervised learning with trainable quantum circuits. We introduce both explicit and implicit approaches. The aim of these approaches is to map data from different classes to separated locations in the Hilbert space via the quantum feature map. We will show that the implicit approach is a generalization of a recently introduced strategy, so-called \textit{quantum metric learning}. In particular, with the implicit approach, the number of separated classes (or their labels) in supervised learning problems can be arbitrarily high with respect to the number of given qubits, which surpasses the capacity of some current quantum machine learning models. Compared to the explicit method, this implicit approach exhibits certain advantages over small training sizes. Furthermore, we establish an intrinsic connection between the explicit approach and other quantum supervised learning models. Combined with the implicit approach, this connection provides a unified framework for quantum supervised learning. The utility of our framework is demonstrated by performing both noise-free and noisy numerical simulations. Moreover, we have conducted classification testing with both implicit and explicit approaches using several IBM Q devices.