Teaching Material

PhD course and slides

Machine Learning from and for Quantum Science

I developed this PhD-level course at Aalto University as a project-based introduction to machine learning and quantum-inspired computational methods for quantum science. The course connects recent research papers to reproducible numerical work: students work in pairs, study one paper in depth, adapt or extend an existing computational workflow, and present both the physics and the implementation in an oral report and a documented code project.

The computational projects are organized around three themes: tensor-network methods for large nonperiodic tight-binding systems, neural quantum states for spin and fermion models, and Hamiltonian-learning inverse problems from simulated spectral data. Each project sheet includes the scientific context, suggested software stack, and concrete simulation tasks.

• Project 1.1: Self-consistent correlated states using tensor networks KPM and QTCI tensor-network methods for self-consistent correlated states and spectral functions in ultra-large nonperiodic tight-binding models.
• Project 1.2: Real-space topology using tensor networks Local topological markers from tensor-network density matrices for ultra-large nonperiodic tight-binding systems.
• Project 1.3: Momentum-resolved spectra in nonperiodic systems using tensor networks QTCI, KPM, and MPO quantum Fourier transforms for local and momentum-resolved spectral functions of quasi-periodic tight-binding models.
• Project 2.1: Neural quantum state tomography and the ANNNI model Neural quantum state tomography with RBMs, followed by a NetKet transverse-field Ising workflow extended to the ANNNI phase diagram.
• Project 2.2: Neural quantum state architectures and the XXZ model Entanglement capacity in neural-network architectures, using the NetKet Heisenberg tutorial as a starting point for the XXZ phase diagram.
• Project 2.3: Neural quantum states for fermions and the spinless t-V model Transformer neural quantum states for molecules and neural-backflow wave functions for the one-dimensional spinless t-V model.
• Project 3.1: Fermionic-chain Hamiltonian learning Nonlocal impurity tomography in a spin-orbit-coupled tight-binding chain, with machine learning used to infer microscopic parameters from spectral fingerprints.
• Project 3.2: Spin-chain Hamiltonian learning DMRGPy spin-chain dynamics and impurity tomography, building spectra-to-couplings training data from matrix-product-state simulations.
• Project 3.3: Molecular quantum magnet learning Setpoint-dependent STM-IETS simulations for a multi-orbital molecular quantum magnet, training a model to infer the spin-orbit coupling.

Master course Lecture notes

Topological Insulators

I prepared and delivered a series of lectures on topological insulators for a master's course in condensed matter physics. The same material was also presented in the Condensed-Matter Educational Seminar, where PhD students lecture for other PhD and advanced master's students. The lectures cover adiabatic transport, Berry phases, Wilson loops, Chern insulators, the Haldane model, edge modes, and symmetry protection.

The material includes my original handwritten notes and an LLM-assisted attempt to transcribe them into typed notes. The typed version is incomplete and still needs to be checked, corrected, and completed.

The exercise sets are meant to be worked through alongside the lecture material. They give concrete problems for practicing the geometric phase formalism, Chern-insulator calculations, and the physical consequences of topology in band systems.

Undergraduate material

Physics solutions and exercises

I wrote a solution set for the undergraduate physics textbook Mazur, E. (2022), Principles and Practice of Physics, published by Pearson.