Public defence, Electronic and Digital Systems, MSc Cristian A. Galvis Florez

Title of the thesis: Quantum methods for reduced-rank Gaussian processes

Thesis defender: Cristian A. Galvis Florez
Opponent: Prof. Matti Silveri, University of Oulu
Custos: Prof. Simo Särkkä, Aalto University School of Electrical Engineering 

Quantum computers can enhance classical methods by performing certain calculations in new, potentially faster ways. This thesis explores how quantum computing can support probabilistic machine learning tools based on Gaussian processes, which are powerful but often too costly to use with large datasets.

The first contribution is in quantum state tomography, which is used to estimate the state of a quantum bit, or qubit. The thesis develops a qubit state tomography method optimized for near-term noisy quantum computers. This helps make quantum devices easier to test, understand, and use in practice.

Gaussian processes enable learning from data and making predictions with quantified uncertainty, but their computational cost increases rapidly as more data is added. This problem can be alleviated by compact feature representations that simplify Gaussian process models and make them more efficient. The second contribution of the thesis is the development of Bayesian Fourier features, a new way to build these reduced-rank approximations for Gaussian processes. Bayesian Fourier features help reduce computational cost while also measuring the uncertainty introduced by the approximation.

Finally, the thesis develops novel quantum-assisted algorithms for Gaussian process regression and Gaussian process quadrature, with particular relevance for fault-tolerant quantum hardware. These methods combine the reduced-rank feature representations mentioned above with quantum algorithms that can process these compact forms efficiently. Instead of depending directly on the number of data points, the proposed approach works with a smaller set of features, which may offer computational advantages when this feature set is much smaller than the full dataset.

Overall, the thesis connects quantum computing with probabilistic machine learning based on Gaussian processes, while making separate contributions to Gaussian process modeling and quantum computing. It shows how quantum methods could help speed up classical prediction tools and highlights practical challenges related to state preparation and implementation on near-term quantum hardware.

Key words: Quantum-assisted algorithms, Gaussian processes, Low-rank kernel approximation, Qubit state tomography, Fourier features

Thesis available for public display 7 days prior to the defence at Aalto University's public display page.

Contact: https://cagalvisf.github.io/