Unsupervised learning

Unsupervised learning is the machine learning task of finding and learning patterns and trends in data based on only unlabelled data.

There are a number of classical and quantum algorithms for different unsupervised learning tasks such as principal component analysis (PCA), clustering, variational autoencoders (VAE), and generative adversarial networks (GAN). In the following page we will focus on GANs.

The focus of much recent research in near term quantum unsupervised learning has been on the quantum analogues of GANs, which are covered in detail in the linked sections:

Quantum generative adversarial networks

Given an a set of data (either classical or quantum) from the probability distribution $P_\text{real}$, generative adversarial networks train a generator, $G_\theta$, and discriminator, $D_\phi$, simultaneously to create samples from $P_G$ that are indistinguishable from $P_\text{real}$. The GAN optimization problem is formalized as:

$G_\theta$ and $D_\phi$ can both be classical or quantum machine learning models.

This is covered in the next page.

References

1. Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., ... & Bengio, Y. (2014). Generative adversarial Networks. Advances in neural information processing systems, 27., doi.org:10.48550/arXiv.1406.2661, arXiv:1406.2661

2. Zoufal, C., Lucchi, A., & Woerner, S. (2019). Quantum generative adversarial networks for learning and loading random distributions. npj Quantum Information, 5(1), 1-9., doi.org:10.1038/s41534-019-0223-2, arXiv:1904.00043

3. Amin, M. H., Andriyash, E., Rolfe, J., Kulchytskyy, B., & Melko, R. (2018). Quantum Boltzmann machine. Physical Review X, 8(2), 021050., doi.org:10.1103/PhysRevX.8.021050), arXiv:1601.02036