Teaching

Lecture: "Quantum Computing 1 & 2" by Prof. J. Wrachtrup, Dr. Florian Kaiser

Quantum Computers and Applications

The goal of the course is to provide a comprehensive overview of the current state-of-the-art quantum computation. The course comprises a lecture (2h/week) plus a tutorial (2h every second week). Students will have the opportunity to do semester projects in which they e.g. work with real quantum computers, learn their programming and use for problem solving.

The module can be selected as elective module in B.Sc., M.Sc. and M.Ed. Physics (9 ETCS) and as area of specialization module in M.Sc. Physics (12 ECTS points) with an additional Quantum Computing internship.

Link to ILIAS
Link to C@MPUS

Module 1: Quantum Computing 1

The physics of information
Landauer’s principle, Reversible Computing, Maxwells demon

Quantum bits
DiVincenco Criteria, Initialization, Gates, Example: P in Si,

Elements of Classical Computer Science
Boolean Algebra and logic gates, Universal computers, Complexity classes,

Quantum Mechanics for Quantum Computation
Quantum mechanics of quantum gates, Relaxation and Dephasing, Density matrix

Quantum gates and first simple algorithm
NOT-, CNOT-Gate, Density matrix tomography, CNOT for spin and ion trap qubits, Deutsch-Jozsa algorithm,

Quantum Error Correction
Error bounds, Majority vote, Stabilizer Formalism, Fault tolerant quantum computing,

Experimental Quantum Error Correction
Majority vote spins, Superconducting Qubits: 5Qubit error detecting code

How to build a Quantum Computer
Superconducting QC, Ion Trap Quantum Computer


^{Figure 1: Image source: IBM}

Module 2: Quantum Computing 2

Shor algorithm
Public Key Cryptography, Period finding, Quantum Fourier Transformation, Implementation of Shor algorithm


^{Figure 2: Image source: iStock}

Quantum Fourier Transformation
Efficient Implementation of QFT, Example: 4 Qubit QFT, Experiments: nuclear magnetic resonance and ion trap quantum computing.

Phase estimation and Grover search algorithm
Precision limits in phase estimation, QFT for phase estimation, Defining oracles for Grover search, example: 3 qubit search.

Quantum random walks
Classical vs. quantum walk, quantum coin, calculate permanent of matrix

^{Figure 3: Image source: AIP}

Quantum Chemistry
Molecular electronic Hamiltonian in 2^nd quantisation, Jordan-Wigner transformation, Trotter decomposition, Components of circuit, Phase estimation for molecular energies, Example: Hydrogen molecule.


^{Figure 4: Image source: Nature}

Quantum classical hybrid algorithm
Variational quantum eigensolver, MaxCut problem,

Introduction to quantum machine learning
k-nearest neighbors, HHL Algorithm, Eigenvalue inversion, Quantum principle component analysis

Quantum communication and Repeaters
Quantum key distribution, Single photon sources, Eckart protocol and CHSH inequality, Quantum memory, lambda-systems, EIT, DLCZ protocol.


^{Figure 5: Image source: QTech Delft}