[Paper Review] A Unified Framework for Quantum Supervised Learning

Nhat A. Nghiem, Samuel Yen-Chi Chen+1 more|arXiv (Cornell University)|Oct 25, 2020

Quantum Computing Algorithms and Architecture47 references25 citations

TL;DR

This paper proposes a unified quantum supervised learning framework using trainable quantum circuits to embed classical data into a Hilbert space, with explicit and implicit approaches for class separation. The implicit method generalizes quantum metric learning, enabling scalable multi-class classification independent of qubit count, and demonstrates robustness with small datasets on both simulations and IBM Q devices.

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 extit{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.

Motivation & Objective

• To unify disparate quantum supervised learning models under a single embedding-based framework.
• To address the scalability limit of existing quantum classifiers in multi-class settings.
• To demonstrate robust performance with small training datasets using near-term quantum hardware.
• To establish a theoretical and practical connection between quantum feature maps and kernel methods.
• To validate the framework on both noisy simulations and real IBM Q quantum processors.

Proposed method

• Proposes an explicit approach that constrains cluster centers to predefined subspaces in Hilbert space for controlled data separation.
• Introduces an implicit approach where cluster centers emerge naturally from optimization, generalizing quantum metric learning.
• Uses parameterized quantum circuits (PQCs) to train the embedding map via gradient-based optimization.
• Employs a quantum feature map to encode classical data into quantum states, enabling non-linear decision boundaries.
• Applies a measurement-based classification strategy where outcomes correspond to predicted labels.
• Validates the framework using both noise-free and noisy simulations, and benchmarks on real IBM Q devices.

Experimental results

Research questions

• RQ1 Can a single framework unify existing quantum supervised learning models through a common embedding mechanism?
• RQ2 How does the implicit approach generalize quantum metric learning to multi-class problems?
• RQ3 What is the performance advantage of the implicit method over explicit methods under small training data regimes?
• RQ4 How do noise and hardware imperfections in NISQ devices affect the classification accuracy of the proposed framework?
• RQ5 To what extent can the number of separable classes exceed the number of qubits in the implicit approach?

Key findings

• The implicit approach generalizes the quantum metric learning method of Lloyd et al. (2020), enabling multi-class classification with arbitrary label counts independent of qubit number.
• The implicit method shows superior robustness to small training sizes, outperforming the explicit method in low-data regimes.
• Numerical simulations confirm high classification accuracy for both explicit and implicit approaches under ideal conditions.
• Experiments on IBM Q devices show good agreement with noisy simulations, though discrepancies emerge under high noise or deep circuits.
• The framework successfully classifies multi-class datasets on real NISQ hardware, demonstrating practical viability for near-term quantum machine learning.
• The explicit approach conceptually unifies prior models such as quantum circuit learning and kernel-based quantum classifiers.