Quantum Computing and Quantum Machine Learning

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

Possible textbooks:

• 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

Interesting online courses and software:

• 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

January 19-23, 2026. Overview of first week, Basic Notions of Quantum Mechanics

• 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

January 26 - January 30, 2026. Composite Systems and Tensor Products

• 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

February 2-6, 2026. Density matrices and Measurements

• 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

February 9-13, 2026. Entanglement and entropies

• 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

February 16-20, 2026. Getting started with the VQE algorithm

• 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.

February 23-27, 2026. Implementing the VQE with measurements and evaluation of gradients

• 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

March 2-6, 2026. VQE for two-qubit systems and the Lipkin model

• 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

March 9-13, 2026. Solving quantum mechanical problems

• 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

March 16-20, 2026. Discussions of project 1 and start discussion of Quantum Fourier transofrms

• 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

March 23-27, 2026

• 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

March 30 - April 3, 2026, Public holiday in Norway no classes

April 6-10, 2026

• Finalizing the QPE discussions, with codes and formalism
• The HHL algorithm for solving linear algebra problems

April 13-17, 2026

• Summing up the HHL discussions, codes and algorithms
• The QAOA algorithm

April 20-24, 2026 Quantum Machine Learning

• Basics of quantum machine learning (QML)
• Quantum Support vector machines (SVM) and classical SVMs

April 27-May 1, 2026 Quantum machine learning

• Quantum neural networks

May 4-8, 2026 Quantum Machine Learning

• Quantum neural networks

May 11-15, 2026

• Quantum neural networks and quantum Boltzmann machines

May 18-22, 2026

• Summary of course and discussion of and work on project 2