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
- 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
- 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
- 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
- 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/2025/NotesJanuary29.pdf
- 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
- 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/2025/NotesFebruary12.pdf
- 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/2025/NotesFebruary19.pdf
- 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/2025/NotesFebruary26.pdf
- Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week6
-
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/2025/NotesMarch5.pdf
-
Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week7
- 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/2025/NotesMarch12.pdf
- 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
- 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/2025/NotesMarch26.pdf
- 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)
- 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.
- 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/2025/NotesApril7.pdf
- 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/2025/NotesApril23.pdf
- 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/2025/NotesApril30.pdf
- 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/2025/NotesMay7.pdf
- 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/2025/NotesMay14.pdf
- Discussion of project 2