Fakultät > Vorlesungen > Sommersemester 2021 > Quantum computing and quantum information

Quantum computing and quantum information

Sommersemester 2021
Dozent: PD Dr. Martin Gärttner
Link zum LSF
75 Teilnehmer/innen

This lecture gives an introduction to topics related to quantum computing and quantum information theory. Video material will be complemented by homework exercises, including programming exercises, and tutorial sessions.

Lecture outline and videos

Course requirements: Basic knowledge of quantum mechanics (Theoretical Physics IV) and basic programming skills are required.
 
Mode of examination: The grade will be based on a written exam.
 
Exam date: The exam will take place online on Monday 26.07.2021 at 14:15h.
 
Notes on homework exercises:
- Please submit the solutions to the exercises by uploading a pdf-scan/photo.
- The exercises can be submitted in teams of 2 people.
- For the programming exercises we will use Python with Jupyter notebooks. We recommend to install Python 3. Installation instructions for Python with Jupyter notebooks can be found at: https://jupyter.readthedocs.io/en/latest/install.html
 
General Literature:
- Nielsen and Chuang: Quantum computation and quantum information 
- Watrous: The Theory of Quantum Information
- Wilde: From Classical to Quantum Shannon Theory
- Bengtsson and Zyczkowski: Geometry of Quantum States
- Lecture notes of John Preskill and corresponding videos
 

Here is an outline of the lecture, as planned so far. Note that this is not a final plan and might be adapted to the participants' needs and interests.

 

Part I: Ideal Quantum Computers

Week 1: The quantum circuit model

Relevant literature:

Nielsen and Chuang, Chapters 2 and 4

Week 2: Introduction to computational complexity and quantum algorithms

Relevant literature:

Nielsen and Chuang Chapters 3.2, 4.5.5, and 1.4.

Lecture 13 of John Preskill’s course

Week 3: The quantum Fourier transform and its applications

Relevant literature:

Nielsen and Chuang Chapters 5.1-5.3

John Preskill’s lecture 14 and 15 and corresponding lecture notes

https://qiskit.org/textbook/ch-algorithms/shor.html

There are pretty good Wikipedia pages about RSA and the Shor algorithm

Week 4: Grover search and quantum simulation

Relevant literature:

Nielsen and Chuang Chapters 4.7 and 6.1

Week 5: Quantum annealing and hybrid quantum-classical algorithms

Relevant literature:

Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation: D. Aharonov et al, SIAM Journal of Computing 37, 166-194 (2007)

Ising formulations of many NP problems, A. Lucas, Front. Phys. 2, 00005 (2014)

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem: E.Farhi et al., Science 292, 472-475 (2001)

Adiabatic Quantum Search in Open Systems, D. S. Wild et al., Phys. Rev. Lett. 117, (2016)

Wolfgang Lechner KITP talk 2016: https://online.kitp.ucsb.edu/online/synquant-c16/lechner/

https://qiskit.org/textbook/ch-applications/qaoa.html

https://qiskit.org/textbook/ch-applications/vqe-molecules.html

A Quantum Approximate Optimization Algorithm: E. Farhi et al., https://arxiv.org/abs/1411.4028

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator: C. Hempel et al., Phys. Rev. X 8, 031022 (2018)

 

Part II: Real Quantum Computers

Week 6: Quantum computing hardware

Erratum: The Molmer Sorensen gate also couples the states 01 and 10 with each other (different from what is claimed in the second video), for details see the original publication listed below.

Relevant literature:

A Quantum Engineer’s Guide to Superconducting Qubits: arXiv:1904.06560

Quantum Computation with Ions in Thermal Motion, Anders Sørensen and Klaus Mølmer. Phys. Rev. Lett. 82, 1971 – Published 1 March 1999

Quantum computing with trapped ions, H.Häffner, C. F. Roos, R. Blatt, Phys. Rep. 469, 155 (2008)

Nielsen and Chuang, Chapter 7.6

Weeks 7+8: Density matrices and quantum channels

Relevant literature:

Nielsen and Chuang Chapters 2.4 and 8.

Week 9: Quantum error correction

Relevant Literature:

Nielsen and Chuang Chapters 10.1-10.3

Week 10: Stabilizer formalism and Fault tolerant quantum computing

Relevant literature:

Nielsen and Chuang Chapters 10.4-10.6

 

Part III: Quantum Information Theory

Week 11: Classical and quantum entropy

Relevant literature: Nielsen and Chuang Chapter 11

Week 12: Pure state entanglement and non-classicality

Relevant Literature:

Nielsen and Chuang Chapters 2.5, 2.6, 11.4.1

Original literature on EPR and Bell (see slides)

Week 13: Mixed state entanglement, entanglement measures

Relevant literature:

Quantum entanglement, Ryszard Horodecki, Pawel Horodecki, Michal Horodecki, Karol Horodecki, https://arxiv.org/abs/quant-ph/0702225

Week 14: Entanglement detection

Relevant literature:

Entanglement detection, Otfried Gühne, Geza Toth, https://arxiv.org/abs/0811.2803

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Quantum computing and quantum information
Sommersemester 2021
Gärttner
Link zum LSF
75 Teilnehmer/innen
Termine