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. Two main themes can be covered:
- Quantum machine learning algorithms, implementations and studies
- Realization and studies of entanglement in physical systems
- 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 to be added https://youtu.be/
- Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/Lectureweek8.pdf
- Quantum Fourier transforms
- Quantum Phase estimation algorithm
- Lab/exercise session: Discussion of project 1 and work on finalizing project
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week9
- Quantum Fourier Transforms, algorithm and implementation
- Quantum phase estimation algorithm
- Setting up circuits for QFTs
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week10
- Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT)
- Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT and QPE.
- Basics of quantum machine learning and discussion of support vector machines
- Quantum phase estimation algorithm (QPE)
- Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT and QPE.
- Basics of quantum machine learning and discussion of support vector machines
- Classical Support Vector Machines, reminder from last week
- Classical Kernels and transition to Quantum Kernels
- Quantum Support Vector Machines
- Quantum support vector machines, theory and code examples
- Quantum neural networks, theory and code examples
- Quantum neural networks, theory and code examples, contn from last week
- Quantum and classical Boltzmann machines
- Summary of course and discussion of project 2