# Quantum Semi-Supervised Kernel Learning

arXiv: https://arxiv.org/abs/2204.10700 · HTML: https://mlsanity.com/paper/2204.10700/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 22 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A quantum-inspired classical algorithm for recommendation systems](https://mlsanity.com/paper/1807.04271/) (2018)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning](https://mlsanity.com/paper/1910.06151/) (2019)
- [Quantum support vector machine for big data classification](https://mlsanity.com/paper/1307.0471/) (2013)
- [Sublinear quantum algorithms for training linear and kernel-based classifiers](https://mlsanity.com/paper/1904.02276/) (2019)
- [Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension](https://mlsanity.com/paper/1811.04909/) (2018)
- [Quantum-inspired algorithms in practice](https://mlsanity.com/paper/1905.10415/) (2019)
- [word2ket: Space-efficient Word Embeddings inspired by Quantum Entanglement](https://mlsanity.com/paper/1911.04975/) (2019)
- [A Survey of Quantum Learning Theory](https://mlsanity.com/paper/1701.06806/) (2017)
- [Quantum-Inspired Support Vector Machine](https://mlsanity.com/paper/1906.08902/) (2019)
- [Quantum Sparse Support Vector Machines](https://mlsanity.com/paper/1902.01879/) (2019)

## Abstract (arXiv)

Quantum computing leverages quantum effects to build algorithms that are faster then their classical variants. In machine learning, for a given model architecture, the speed of training the model is typically determined by the size of the training dataset. Thus, quantum machine learning methods have the potential to facilitate learning using extremely large datasets. While the availability of data for training machine learning models is steadily increasing, oftentimes it is much easier to collect feature vectors that to obtain the corresponding labels. One of the approaches for addressing this issue is to use semi-supervised learning, which leverages not only the labeled samples, but also unlabeled feature vectors. Here, we present a quantum machine learning algorithm for training Semi-Supervised Kernel Support Vector Machines. The algorithm uses recent advances in quantum sample-based Hamiltonian simulation to extend the existing Quantum LS-SVM algorithm to handle the semi-supervised term in the loss. Through a theoretical study of the algorithm's computational complexity, we show that it maintains the same speedup as the fully-supervised Quantum LS-SVM.