Applied Quantum Mechanics

This module is an introduction into the numerous applications of quantum mechanics that have emerged in recent years. After introducing the language of quantum information processing it will cover various applications such as

• simple quantum algorithms for quantum computers
• atomic clocks and GPS
• superconducting SQUID magnetic field sensors for sensing of currents in the brain
• protocols of nuclear magnetic resonance spectroscopy and their application in biochemistry
• NV centers in diamond and their potential use for imaging of the magnetic fields of single molecules, hard disk write heads and neuronal currents.
• decoherence of quantum systems; what it is, how it arises and how it can be mitigated in applications.

After passing the module students are able to 

• understand the definition of a qubit
• understand the most prominent implementations of qubits 
• understand the description of quantum manipulations as a circuit and as a quantum control protocol
• understand the most prominent applications of qubits as quantum sensors
• understand and apply the semiclassical model of light-matter interaction
• understand simple quantum algorithms for computation and error correction
• analyze superconducting quantum circuits using the Josephson equations 
• analyze decoherence using the density matrix
• create and visualize quantum control protocols to control the time evolution of a qubit and to prepare specific quantum states

• basic knowledge of quantum mechanics of Bachelor level

Teaching in this module is based on three components

Lecture

In the thematically structured lecture the learning content is presented. With cross references between different topics the universal concepts in physics are shown. In scientific discussions the students are involved to stimulate their analytic-physics intellectual power.

In the exercise the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.

Some lectures are taught in "flipped classroom format". Students will be asked to watch a webcast of the lecture, think about questions to ask, and discuss them with the lecturer in the following lecture. 

Homework

A homework of typically two to three exercises is assigned every week. These exercises are closely linked to the lecture and demand considerable effort. 

Exercises

The solution to the homework is presented and discussed in a weekly exercise class. This event is led by an experienced PhD student or postdoc and equally serves as a forum to discuss any question relating to both the lecture and the homework. 

Blackboard/Powerpoint, 80%/20% respectively.

M. Nielsen / I. Chuang - Quantum Computation and Quantum Information, Cambridge University Press, 2000

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

• Design of a quantum protocol to prepare a specific quantum state.
• Computing the time evolution of a qubit under a quantum control sequence.
• Analyzing decoherence of a qubit by the density matrix.

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.