The first part of the course (project 1 and till mid march) has its focus on studies of quantum-mechanical many-particle systems using quantum computing algorithms and quantum computers. The second part is optional and depends on the interests and backgrounds of the participants. The lectures cover mainly quantum machine learning algorithms with an emphasis on variational quantum algorithms for NISQ-era quantum computers. We discuss for example quantum for neural networks, quantum support vector machines, quantum Boltzmann machines and the QAOA algorithm. Fault-tolerant algorithms like quantum Fourier transforms, quantum phase estimation and the HHL algorithm are also discussed.
- Advanced VQE and hamiltonian systems
- Maria Schuld and Francesco Petruccione, Machine Learning with Quantum Computers, see https://link.springer.com/book/10.1007/978-3-030-83098-4
- Wolfgang Scherer, Mathematics of Quantum Computing, see https://link.springer.com/book/10.1007/978-3-030-12358-1
- Hidary, Quantum Computing: An Applied Approach, see https://link.springer.com/book/10.1007/978-3-030-23922-0
- Robert Hundt, Quantum Computing for Programmers, https://www.cambridge.org/core/books/quantum-computing-for-programmers/BA1C887BE4AC0D0D5653E71FFBEF61C6
- Claudio Conti, Quantum Machine Learning (Springer), https://link.springer.com/book/10.1007/978-3-031-44226-1
- Robert Loredo, Learn Quantum Computing with Python and IBM Quantum Experience, see https://github.com/PacktPublishing/Learn-Quantum-Computing-with-Python-and-IBM-Quantum-Experience
- Stefano Olivares, A Student’s Guide to Quantum Computing, see https://link.springer.com/book/10.1007/978-3-031-83361-8
- IBM's Quantum Computer Programming: Hands-On Workshop at https://quantgates.com/learn-quantum
- QuTip at https://github.com/qutip and https://qutip.org/
- QisKit at https://www.ibm.com/quantum/qiskit
- PySCF for traditional quantum mechanical methods at https://pyscf.org/user/install.html#how-to-install-pyscf. This library can be integrated with QisKit for quantum computing simulations.
- Qbraid at https://www.qbraid.com
- PennyLane at https://pennylane.ai/ (tailored to machine learning)
Time: Each Wednesday at 1015am-12pm CET and exercise sessions 815-10am (The lecture sessions will be recorded)
-Permanent Zoom link for the whole semester is https://uio.zoom.us/my/mortenhj
- Definitions, Linear Algebra reminder, Hilbert Space, Operators on Hilbert Spaces, Composite Systems
- Definitions
- Mathematical notation, Hilbert spaces and operators
- Description of Quantum Systems and one-qubit systems
- States in Hilbert Space, pure and mixed states
- Video of lecture at https://youtu.be/J5lK-fTcTYY
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/HandWrittenNotes/2026/Lectureweek1.pdf
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week1
- Reading recommendation: Scherer chapter 2 and/or Hidary chapter 12
- Spectral decomposition and measurements
- Density matrices
- Entanglement, pure and mixed states
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week2
- Reading recommendation: Scherer chapter 2 and sections 3.1-3.3. Hundt, Quantum Computing for Programmers, chapter 2.1-2.5. Hundt's text is relevant for the programming part where we build from scratch the ingredients we will need.
- Video of lecture at https://youtu.be/KgMw2lC-oJY
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek2.pdf
- Density matrices, entanglement and entropies
- Video of lecture at https://youtu.be/xkbXx6XIlvU
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek3.pdf
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week3
- Reminder from last week on entanglement, density matrices and entropies
- One-qubit and two-qubit gates, background and realizations
- Simple Hamiltonian systems and getting started with the first project
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week4
- Reading recommendation: For the discussion of one-qubit, two-qubit and other gates, sections 2.6-2.11 and 3.1-3.4 of Hundt's book Quantum Computing for Programmers, contain most of the relevant information.
- Video of lecture at https://youtu.be/4Ew5UNHnsdM
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek4.pdf
- Quantum gates and operations and simple quantum algorithms
- Discussion of the VQE algorithm and discussions of project 1
- Simple one-qubit and two-qubit Hamiltonians
- Video of lecture at https://youtu.be/f9AfWyGWbCI
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lecturesweek5.pdf
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week5. See in particular the additional jupyter-notebooks for the one- and two-qubit cases. For those of you who wish to test IBM's quantum computers with Qiskit, there are similar notebooks.
- Reading recommendation: For the discussion of one-qubit, two-qubit and other gates, sections 2.6-2.11, 3.1-3.4 and 6.11.1-.6.11.3 of Hundt's book Quantum Computing for Programmers, contain most of the relevant information.
- VQE and adaptive VQE, Variational Quantum Eigensolver and discussion of codes
- Simulations of of Hamiltonians, focus on the one- and two-qubit Hamiltonians
- Start discussions of Lipkin model
- Video of lecture at https://youtu.be/MVLbBcTPwqg
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek6.pdf
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week6
- Implementing the VQE algorithm for the two-qubit and Lipkin-model Hamiltonians.
- Video of lecture at https://youtu.be/g-hKlUYxfcw
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek7.pdf
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week7
- Lipkin model and VQE
- Jordan-Wigner transformation and other Hamiltonians as examples
- Start discussion of Quantum Fourier Transforms
- Lab/exercise session: work on project 1
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week8
- Video of lecture at https://youtu.be/C8vxBY-AmD8
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek8.pdf
- Quantum Fourier transforms
- Lab/exercise session: Discussion of project 1 and work on finalizing project 1
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week9
- Video of lecture at https://youtu.be/qQw4zme7LyI
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek9.pdf
- Quantum Fourier Transforms, algorithm and implementation
- Quantum phase estimation (QPE) algorithm
- Setting up circuits for QFTs and the QPE and discussion of codes
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week10
- Video of lecture at https://youtu.be/hNiFE2OWdIg
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek10.pdf
- Finalizing the QPE discussions, with codes and formalism
- The HHL algorithm for solving linear algebra problems
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week11, see PDF file and jupyter-notebook. The jupyter-notebook is a companion to the PDF file
- Video of lecture at https://youtu.be/Rsn2INejK7o
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek11.pdf
- The HHL algorithm, codes and algorithms
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week12, see PDF file and jupyter-notebook. The jupyter-notebook is a companion to the PDF file
- Video of lecture at https://youtu.be/e70HFOTKKMg
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek12pdf
- QAOA algorithm and implementation
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week13, see PDF file and jupyter-notebook. The jupyter-notebook is a companion to the PDF file
- Basics of quantum machine learning (QML)
- Quantum neural networks (QNN) and links to QAOA and other methods
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week14, see PDF file and jupyter-notebook. The jupyter-notebook is a companion to the PDF file
- Video of lecture at https://youtu.be/0iTYdjBgQcA
- Quantum neural networks and Quantum Physics Informed Neural Networks (QPINNs)
- Solving differential equations with QPINNs
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week15, see PDF file and jupyter-notebook. The jupyter-notebook is a companion to the PDF file
- Video of lecture at https://youtu.be/WSlS4-xRwCI
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek15.pdf
- Quantum neural networks and quantum Boltzmann machines
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week16, see PDF file and jupyter-notebook. The jupyter-notebook is a companion to the PDF file
- Video of lecture at https://youtu.be/PaBRCA3icW4
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek16.pdf
- Quantum Boltzmann machines (continued from previous week) and summary of course and discussion of and work on project 2
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week17, see PDF file and jupyter-notebook. The jupyter-notebook is a companion to the PDF file
- Video of summary lecture at https://youtu.be/us6iGf1niBE