Lecture Quantum Information and Computation (Summer 2022)
Type: 
Lecture with Exercises 
Programs: 
MSc ITS, AI, Math, Physics and CASA PhD Lectures 
Lecturer: 
Michael Walter

Time and Place: 
Lectures: Tue 1416 (GD 03/150) Exercises: Thu 1416 (GABF 05/608)

First meeting: 
Apr 5 
Credits: 
5 CP 
Contact time: 
2+2 SWS SWS 
Language: 
English 
Course number: 

Links: 
Moodle,
VVZ

Course Description & Tentative Syllabus
This course will give an introduction to quantum information and quantum computation from the perspective of theoretical computer science.
We will discuss the mathematical model of quantum bits and circuits, how to generalize computer science concepts to the quantum setting, how to design and analyze quantum algorithms and protocols for a variety of computational problems, and how to prove complexity theoretic lower bounds.
Topics to be covered will likely include:
 Fundamental axioms of quantum mechanics: from classical to quantum bits
 Fewqubit protocols: teleportation and nocloning
 The power of entanglement: Bell inequalities and CHSH game
 Quantum circuit model of computation
 Basic quantum algorithms: DeutschJozsa, BernsteinVazirani, Simon
 Grover’s search algorithm and beyond
 Quantum Fourier transform and phase estimation
 Shor’s factoring algorithm
 Quantum query lower bounds
 Quantum complexity theory
 Quantum probability: mixed states, POVM measurements, quantum channels
 Quantum entropy and Holevo bound
 Quantum error correction
 Quantum cryptography
 Quantum “supremacy”
This course should be of interest to students of computer science, mathematics, physics, and related disciplines (including those who previously followed the Bachelor’s course Quantenalgorithmen by Prof. May).
Students interested in a Master’s thesis in quantum information / computing / cryptography / … are particularly encouraged to participate.
If you are participating in this course you might also be interested in our seminar.
Recommended prior knowledge
Familiarity with linear algebra (in finite dimensions) and probability (with finitely many outcomes) at the level of a first Bachelor’s course;
we will briefly remind you of the more difficult bits in class.
In addition, some mathematical maturity, since we will discuss precise mathematical statements and rigorous proofs.
No background in physics is required!
Literature
 Handwritten lecture notes (and video recordings of the lectures) will be provided
In addition, the following references can be useful for supplementary reading (the first two in particular served as inspiration for this course):
 O’Donnell, Quantum Computation and Quantum Information, course material (2018)
 de Wolf, Quantum Computing: Lecture Notes, arxiv:1907.09415 (2022)
 Nielsen and Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010)
 Mermin, Quantum Computer Science, Cambridge University Press (2007)
Learning outcomes
You will learn fundamental concepts, algorithms, and results in quantum information and computation theory.
After successful completion of this course, you will know the mathematical model of quantum information and computation, how to generalize theoretical computer science concepts to the quantum setting, how to design and analyze quantum algorithms and protocols for a variety of computational problems, and how to prove complexity theoretic lower bounds.
You will be prepared for an advanced course or a research or thesis project in this area.
Grades and homework
To get credit for this course, you have to pass the final exam.
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