# Quantum Semi-Supervised Learning with Quantum Supremacy

arXiv: https://arxiv.org/abs/2110.02343 · HTML: https://mlsanity.com/paper/2110.02343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 5 Oct 2021.

## Builds on (most cited first, 3 of 3)

- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- [Quantum Cross Entropy and Maximum Likelihood Principle](https://mlsanity.com/paper/2102.11887/) (2021)
- [Quantum Data Compression and Quantum Cross Entropy](https://mlsanity.com/paper/2106.13823/) (2021)

## Abstract (arXiv)

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.