The websiate for this set of lectures is https://github.com/CompPhysics/QuantumComputingLectures. Feel free to navigate the different folders and use as you like.
The aim of this set of lectures is to demonstrate how we can use quantum computing to find for example the eigenvalues and eigenstates of quantum mechanical many-body systems. After having introduced some of the basic notations and formalism (see below), we focus on how to implement the Variational Quantum Eigensolver (VQE) algorithm for finding the eigenvalues of selected Hamiltonians. We will focus on a well-studied model for the Hamiltonian, the so-called Lipkin model. Using this model we will show how to find the eigenvalues. Hands-on jupyter-notebooks will be used to demonstrate how one can simulate such quantum mechanical systems, using either own codes or the functionality provided by a software like Qiskit https://qiskit.org/.
The lectures will also serve as a wy to motivate physical realization (quantum engineering) of different circuits and gates.
- Mathematical notation, Hilbert spaces and operators
- Description of Quantum Systems and one- and many-qubit systems
- States in Hilbert Space, pure and mixed states
- Operators and gates
- Spectral decomposition and measurements
- Density matrices
- Entanglement and Schmidt decomposition
- Quantum Entropy
- Variational Quantum Eigensolver (VQE)
- Solving eigenvalue problems using the VQE
- Implementing VQE efficiently for Hamiltonian models (Lipkin model)
The notes (either in pdf, html or as jupyter-notebooks) can be accessed from https://github.com/CompPhysics/QuantumComputingLectures.