Learning properties of parametrized quantum states: Practical algorithms with theoretical guarantees

Licentiatavhandling, 2026

The analysis of quantum state properties is of fundamental importance in quantum physics and serves as a primary motivation for the development of quantum computing. In particular, low-temperature and ground states are of significant interest, as they most prominently exhibit phenomena unique to quantum mechanics. However, extracting such properties typically requires costly numerical simulations or laboratory experiments, while simulation on quantum hardware remains limited by the capabilities of current devices. This thesis proposes two complementary approaches to address these challenges.

The first contribution presents an algorithm for predicting ground-state properties across an entire family of quantum states within the same phase of matter, based on training data. Under slightly stronger assumptions, we improve upon the sample complexity of existing methods, prove the same rigorous guarantees for a deep neural network-based approach, and demonstrate its practical advantages through extensive numerical experiments.

The second contribution addresses the challenge of preparing quantum states of interest using Variational Quantum Algorithms (VQAs), a framework based on the classical optimization of parametrized quantum circuits. We introduce multi-armed stochastic bandits into this setting, propose an instance-optimal algorithm for continuous single-parameter optimization, and and motivate further exploration of the framework we introduced with an array of experiments.