Quantum Computing
Quantum mechanics has fundamentally revolutionized our understanding of fundamental physical laws and provides the explanation of many technologically useful systems and effects, such as semiconductors and lasers. Nevertheless, information in today´s computers is essentially processed according to the laws of classical physics. Quantum computers are computing machines whose functionality specifically uses quantum phenomena such as superposition and entanglement. Because of this fundamental extension, quantum computers are capable of computations that classical computers cannot handle with realistic effort, e. g. the factorization of large numbers, the search in large databases, as well as the simulation of quantum systems such as molecules or solids. This lecture provides an introduction into the theory of quantum computers, including concepts such as quantum bits, the quantum circuit model, quantum gates, and complexity theory. We will study the most important known quantum algorithms: the Shor factorization algorithm, the Grover algorithm for database search, and the Harrow-Hassidim-Lloyd algorithm for solving linear systems of equations. We also introduce the concept of quantum simulation, i. e., the simulation of quantum mechanical systems on a quantum computer. In this context, hybrid algorithms are considered, which are composed of classical and quantum parts. The physical realization of quantum computers requires methods for quantum error correction, which we also introduce in this lecture. Participants can implement quantum algortihms on the IBM-Q quantum computer on their own.
(Prerequisite: First course in Quantum Mechanics, physics IK4)
lecture:
| Professor | Termin / schedule | Raum / room |
|---|---|---|
| Prof. Dr. Guido Burkard | Mon 08.15-09.45 (new time) | P603 |
| Fri 10.00-11.30 | P603 |
first lecture: Monday, 11 April 2022, 10:00 h, P603
exercises: (2 hrs./week):
| exercises | Tutor | schedule | room |
|---|---|---|---|
| Dr. Regina Finsterhoelzl ( Exercise coordinator) | |||
| G1 | Benedikt Tissot | Thu 8:15 - 9:45 | P602 |
| G2 | Dr. Joris Kattemölle | Thu 13:30 - 15:00 | P602 |
Contents
- Introduction (Bits and Qubits, classical and quantum complexity)
- Quantum circuits
- Quantum Fourier Transform (Shor algorithm, discrete logarithm, hidden subgroup problem)
- Quantum search (Grover algorithm, amplitude amplification)
- Quantum error correction (Codierung, fehlertolerantes Rechnen, topologische Codes)
- Quantum simulation
- Hybrid quantum-classical algorithms (VQE, QAOA)
Exam
requirements (Master's degree): oral exam plus participation in lecture and exercises
minimal requirement for admission to exam: 50% of exercises worked out, 2x presenting at the blackboard
note: exercises need to be redone for admission to exam also when repeating the course
Literature
Quantum information (general)
- M. A. Nielsen & I. L. Chuang, Quantum Computation and Quantum Information (Cambridge, 2001; neue Auflage 2011)
- M. D. Mermin, Quantum Computer Science (Cambridge, 2007)
- J. Preskill, Lectures Notes for Physics 229: Quantum Information and Computation,
http://www.theory.caltech.edu/people/preskill/ph229/ - R. de Wolf, Quantum Computing: Lecture Notes, https://arxiv.org/pdf/1907.09415.pdf
- A. Yu. Kitaev, A. H. Shen, M. N. Vyalyi, Classical & Quantum Comp. (AMS 2002)
- S. Aaronson, Quantum Computing since Democritus (Cambridge, 2013)
- E. G. Rieffel & H. Polak, Quantum Computing (MIT Press, 2011)