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
• 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

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
• 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
• QuTip at https://qutip.org/
• PennyLane at https://pennylane.ai/

Time: Each Wednesday at 215pm-4pm CET and exercise sessions 4pm-5pm (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/YRobDADb63E
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week1
  • Reading recommendation: Scherer chapter 2

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

• Spectral decomposition and measurements
• Density matrices
• Entanglement, pure and mixed states v- 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/T7l-rciM0N0
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesJanuary29.pdf

February 2-6, 2026. Density matrices and Measurements

• Discussion of gates and project 1
• Quantum gates and circuits
• Developing our own codes for Bell states and comparing with qiskit
• 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 gates and circuits
• One-qubit and two-qubit gates, background and realizations
• Simple Hamiltonian systems
• 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/UcfOVvFyw2E
  • Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesFebruary12.pdf

February 16-20, 2026.

• Entanglement and Schmidt decomposition
• Entropy as a measurement of entanglement
• Simple one-qubit and two-qubit Hamiltonians
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week5
  • 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.
• Video of lecture at https://youtu.be/caR8AQM6Rwo
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesFebruary19.pdf

February 23-27, 2026. Quantum gates and circuits and Quantum Fourier Transform and Hamiltonians

• Quantum gates and operations and simple quantum algorithms
• Discussion of the VQE algorithm and discussions of project 1
• Video of lecture at https://youtu.be/13JyMS50beg/
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesFebruary26.pdf
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week6

March 2-6, 2026. Algorithms for solving quantum mechanical problems.

• 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/jGtcEc85VbE

• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesMarch5.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
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week8
• Video of lecture at https://youtu.be/hdUnJcJGigw
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesMarch12.pdf

March 16-20, 2026. Discussions of project 1 and work on the VQE

• Lipkin model and VQE
• 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

March 23-27, 2026

• Quantum Fourier Transforms, algorithm and implementation
• Quantum phase estimation algorithm
• Video of lecture at https://youtu.be/UHqBk1eQT6E
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesMarch26.pdf
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week10

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

April 6-10, 2026

• Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT)
• Quantum Fourier transforms (QFTs), reminder from last week
• Setting up circuits for QFTs
• Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT and QPE.

April 13-17, 2026

• Setting up circuits for QFTs
• Quantum phase estimation algorithm (QPE)
• Reading recommendation Hundt, Quantum Computing for Programmers, sections 6.1-6.4 on QFT and QPE.
• Video of lecture at https://youtu.be/3myI1qFLVN8
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesApril7.pdf

April 20-24, 2026 Quantum Machine Learning

• Basics of quantum machine learning and discussion of support vector machines
• Video of lecture at https://youtu.be/C36Kg4eaO7A
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesApril23.pdf

April 27-May 1, 2026 Quantum machine learning

• Classical Support Vector Machines, reminder from last week
• Classical Kernels and transition to Quantum Kernels
• Quantum Support Vector Machines
• Video of lecture at https://youtu.be/L-c4EBMinwM
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesApril30.pdf

May 4-8, 2026 Quantum Machine Learning

• Quantum support vector machines, theory and code examples
• Quantum neural networks, theory and code examples
• Video of lecture, first part at https://youtu.be/L9kvkEW1ZgQ
• Video of lecture, second part with discussion of codes at https://youtu.be/73V0LipuHac
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesMay7.pdf

May 11-15, 2026

• Quantum neural networks, theory and code examples, contn from last week
• Quantum and classical Boltzmann machines
• Video of lecture at https://youtu.be/icHV-pgq6uQ
• Whiteboard notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2026/NotesMay14.pdf

May 18-22, 2026

• Discussion of project 2