• 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

-Permanent Zoom link for the whole semester:

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

• 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
  • Link to video of lecture https://youtu.be/YRobDADb63E
• 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

• Tensor products of Hilbert Spaces and definition of Computational Basis
• Simple Hamiltonians and other operators
• States and Observables for Composite systems
• Quantum operations, circuits and gates
• 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 2

• 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, xxx

• More on density matrices and measurements

• Entanglement and Schmidt decomposition

• Review of Schmidt decomposition and entanglement

• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week4

  • Reading recommendation: Scherrer, Mathematics of Quantum Computations, xxx

• Entropy and density matrices
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week5

• 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

• 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

• 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

• VQE and Qiskit
• Teaching material in different formats at https://github.com/CompPhysics/QuantumComputingMachineLearning/tree/gh-pages/doc/pub/week9

• Solving eigenvalue problems with and without Qiskit.
• 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

• 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