Quantum Semi-Supervised Learning with Quantum Supremacy

TL;DR

This paper introduces quantum semi-supervised learning frameworks that address data scarcity and computational limits, demonstrating quantum supremacy in matrix operations and specific learning algorithms.

Contribution

It proposes a novel quantum semi-supervised learning framework and a systematic protocol for designing quantum algorithms with quantum supremacy, extending beyond semi-supervised learning.

Findings

Naive quantum matrix product estimation outperforms classical algorithms.

Quantum semi-supervised algorithms show quantum supremacy in time complexity.

Two concrete quantum semi-supervised algorithms are demonstrated.

Abstract

Quantum machine learning promises to efficiently solve important problems. There are two persistent challenges in classical machine learning: the lack of labeled data, and the limit of computational power. We propose a novel framework that resolves both issues: quantum semi-supervised learning. Moreover, we provide a protocol in systematically designing quantum machine learning algorithms with quantum supremacy, which can be extended beyond quantum semi-supervised learning. In the meantime, we show that naive quantum matrix product estimation algorithm outperforms the best known classical matrix multiplication algorithm. We showcase two concrete quantum semi-supervised learning algorithms: a quantum self-training algorithm named the propagating nearest-neighbor classifier, and the quantum semi-supervised K-means clustering algorithm. By doing time complexity analysis, we conclude that they indeed possess quantum supremacy.