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

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
• 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

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 to be added:

January 20-24, 2025. 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
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week1
  • Reading recommendation:

January 27 - January 31, 2025. Composite Systems and Tensor Products

• Spectral decomposition and measurements
• Density matrices
• Simple Hamiltonians and other operators
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week2
  • Reading recommendation:

February 3-7, 2025. Density matrices and Measurements

• Spectral decomposition and measurements
• Density matrices
• Entanglement and Schmidt decomposition
• Entropies
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week3
  • Reading recommendation:

February 10-14, 2025. Entanglement and entropies

• Entanglement and Schmidt decomposition
• Entropy as a measurement of entanglement
• Introduction to gates and calculations
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week4
  • Reading recommendation:

February 17-21, 2025.

• 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/week5

February 24-28, 2025. 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
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week6

March 3-7, 2025. 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-qubit Hamiltonian
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week7

March 10-14, 2025. Solving quantum mechanical problems

• Discrete Fourier transforms and fast Fourier transform
• Quantum Fourier transforms
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week8

March 17-21, 2025. Second quantization and Hamiltonians for quantum computing, discussion of the Lipkin model

• Quantum Fourier Transforms, algorithm and implementation
• Quantum phase estimation algorithm
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week9

March 24-28, 2025

• TBA

March 31-April 4, 2025

• TBA

April 7-11, 2025

• TBA

April 14-18, 2025, Public holidays in Norway no classes

April 21-15, 2025

• TBA

April 28-May 2, 2025

• TBA

May 5-9, 2025

• TBA

May 12-16, 2025

• TBA
• Summary of course