Quantum Computing and Quantum Machine Learning

Recommended 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

Time: Each Monday at 1215pm-2pm CET (The sessions will be recorded)

-Permanent Zoom link for the whole semester:

• https://msu.zoom.us/j/6424997467?pwd=ZW5jSGtEeHJxM0dqd0draXlWY29FQT09
• Meeting ID: 642 499 7467
• Passcode: FYS4411

January 23-27, 2023. Overview of first week, Basic Notions of Quantum Mechanics

• Definitions, Linear Algebra reminder, Hilbert Space, Operators on Hilbert Spaces, Composite Systems and more

  • Definitions
  • Mathematical notation, Hilbert spaces and operators
  • Description of Quantum Systems and one-qubit systems
  • States in Hilbert Space, pure and mixed states
  • Operators and gates

• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week1

  • Reading recommendation: Scherer, Mathematics of Quantum Computations, chapter 2

• Video of lecture at https://youtu.be/ktZSFYIoNVM

• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesJanuary23.pdf

January 30 - February 3, 2023. Composite Systems and Tensor Products

• Tensor products of Hilbert Spaces and definition of Computational Basis
• Simple Hamiltonians and other operators
• States and Observables for Composite systems
• Quantum operations
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week2
  • Reading recommendation: Scherer, Mathematics of Quantum Computations, chapter 3
• Video of lecture at https://youtu.be/ucXpNSISzOw
• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesJanuary30.pdf

February 6-10, 2023. Density matrices and Measurements

• Spectral decomposition and measurements
• Density matrices
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week3
  • Reading recommendation: Scherer, Mathematics of Quantum Computations, chapters 2 and 3
• Video of lecture at https://youtu.be/jVh_0KfSSNk
• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesFebruary6.pdf

February 13-17, 2023. Entanglement and entropies

• More on density matrices and measurements
• Entanglement and Schmidt decomposition
• Start discussion of Entropies
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week4
  • Reading recommendation: Scherrer, Mathematics of Quantum Computations, chapter 4
• Video of lecture at https://youtu.be/QVPQmeSAX8M
• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesFebruary13.pdf

February 20-24, 2023.

• Review of Schmidt decomposition and entanglement from last week, see jupyter-notebook at URL:"https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/pub/week4/ipynb/week4.ipynb"
• More on entanglement
• Entropy and traces of density matrices
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week5
  • Reading recommendation: Scherer, Mathematics of Quantum Computations, section 2.3 and chapter 4
  • Video of lecture at https://youtu.be/gnlGUjKGDts
  • Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesFebruary20.pdf

February 27-March 3, 2023. Quantum gates and circuits and Quantum Fourier Transform and Hamiltonians

• Quantum gates and operations and simple quantum algorithms

• Quantum Fourier Transforms

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

  • Video of lecture at https://youtu.be/IkD0fiBhxd0
  • Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesFebruary27.pdf

March 6-10, 2023. Algorithms for solving quantum mechanical problems.

• Introduction of Hamiltonians to study, the Lipkin model
• Quantum Phase estimation algorithm
• VQE, Variational Quantum Eigensolver
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week7
  • Video of lecture at https://youtu.be/uf9xwcl2IEE
  • Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesMarch6.pdf

March 13-17, 2023. Solving quantum mechanical problems

• Analyzing the solution of eigenvalue problems using the Lipkin model
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week8
  • Video of lecture at https://youtu.be/ffIwxiUJGT4
  • Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesMarch13.pdf

March 20-24, 2023. Second quantization and Hamiltonians for quantum computing, discussion of the Lipkin model and

and project 1

• VQE and Qiskit
• Discussion of 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/ZKv8pEy3Y_4

March 27-31, 2023. VQE and project discussion

• Solving eigenvalue problems with and without Qiskit.
• Discussion of project 1
• Reading recommendation Hundt, Quantum Computing for Programmers, chapter 6, in particular section 6.1
• See also VQE review article at https://www.sciencedirect.com/science/article/pii/S0370157322003118?via%3Dihub
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week10
• Video of lecture at https://youtu.be/JT5bjAQyS4k
• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesMarch27.pdf

April 17-21, 2023. VQE and project discussion

• Implementing VQE efficiently and studies of the Lipkin model
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week11
• Video of lecture at https://youtu.be/lTB5I1vkdlw
• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesApril17.pdf

April 24-28, 2023. VQE and project discussion, introducing Quantum Fourier Transforms

• Wrapping up material on VQE
• Discussion of Quantum Fourier Transforms and Quantum Phase estimation algorithms
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week12
• Video of lecture at https://youtu.be/5bgNXjaP8y4
• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesApril24.pdf
• Reading suggestion: Hundt sections 6.2-6.4

May 1-5, 2023. Public holiday, no lecture on May 1

May 8-12, 2023. Quantum Fourier transforms

• Discussion of Quantum Fourier Transforms and Quantum Phase estimation algorithms
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week13
• Video of lecture at TBA
• Reading suggestion: Hundt sections 6.2-6.4
• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesMay8.pdf
• Lecture moved to Friday

May 15-19, 2023. Last session and summary of course

• Discussion of final project and summary of course
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week14
• Video of lecture at TBA
• Handwritten notes at https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2023/NotesMay15.pdf

May 22-26, 2023. Project work and discussion

• Discussion of project if there is interest