Lecture/QIT I SS11

From MPQTheory

Quantum Information Theory I

Prof. Dr. J. I. Cirac with Dr. G. Giedke

Lecture: Fr 14:15h - 16h

starting May 13th: MPI für Quantenoptik, H.-Kopfermann-Str. 1, B0.21 (on May 13th: B0.22)

Changes in time:

• on Fri, Jun 10, the lecture will be from 10:00-12:30h in B0.22 (or some other room to be announced)
• on Fri, Jun 17 and 24 there will be no lecture
• on Fri, Jul 01, the lecture will be again as usual 14:15-16:30h in B0.21
• on Fri, Jul 08, the lecture will from 17:30-19:30h in B0.21

The lecture provides an introduction to the theory of quantum information and computation. The basic concepts and tools of processing quantum information are introduced and it is shown how they can be used to exploit quantum features for enhanced information processing.

Contents 1 Outline 2 Requirements: 3 Literature: 4 Exercises 5 Contact

Outline

1. Introduction
   1. a different kind of information (historical sketch, impossible and possible machines)
   2. elements of quantum information processing (qubits, quantum gates, quantum circuits)
2. Quantum Computation
   1. Computational Complexity (see, e.g. The Complexity Zoo or these lecture notes for further information)
   2. Models of Quantum Computation (circuit model, adiabatic quantum computing, one-way quantum computer)
      1. Quantum Circuit Model: universal set of gates, equivalence of universal sets (see, e.g., Lecture Notes by A. Childs), difficulty of approximating general unitaries
   3. Quantum Algorithms
      1. black box algorithms: Deutsch-Jozsa, Simon (see, e.g., [ J. Watrous, ])
      2. quantum Fourier transform, period finding, factoring (further reading: A. Childs and W. van Dam, Quantum algorithms for algebraic problems, RMP 82, 1 (2010); quant-ph/0812.0380)
      3. quantum search (further reading: Ambainis, Quantum search algorithms, quant-ph/0504012)
      4. quantum simulation
      5. recent developments and perspectives
3. Entanglement Theory (time permitting)
   1. classification, criteria, measures, entanglement transformations
4. Quantum Communication (time permitting)
   1. quantum channels
   2. quantum cryptography
   3. communication complexity
5. Quantum Error Correction (time permitting)
   1. quantum operations (Kraus representation, complete positivity, Choi-Jamiolkowski isomorphism)
   2. error correction conditions, error correcting codes
   3. fault-tolerance, threshold theorem
   4. quantum memory
6. Implementations of Quantum Information Processing

Requirements:

Quantum Mechanics, Linear Algebra

Literature:

• Quantum Computation:
  • Nielsen and Chuang, Quantum Information, Cambridge University Press (Errata list)
  • R. F. Werner, Quantum Information Theory - An Invitation
  • J. Preskill, Lecture Notes QIT
  • J. Gruska, Quantum Computing, McGrawHill
  • European QIPC roadmap
  • US Quantum Computation Roadmap
• Complexity Theory:
  • C. Papadimitriou, Computational Complexity, Addison-Wesley 1995.
• Entanglement Theory
  • Horodecki et al. Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009) (or arXiv:quant-ph/0702225).
• Quantum Communication
  • M. Hayashi Quantum Information Springer, 2006. (ch. 4 and 10)
  • Alleaume et al., SECOQC White Paper on Quantum Key Distribution and Cryptography arXiv:quant-ph/0701168 or Renner, Beweisbare Sicherheit durch Quantenkryptografie, Information Technology 49(2) 127 (2007).
  • Buhrman et al., Non-locality and Communication Complexity, Rev. Mod. Phys. 82 665–698 (2010) (or: arXiv:0907.3584).
• Quantum Error Correction
  • Knill et al., Introduction to Quantum Error Correction, quant-ph/0207170 (non-technical introduction)
  • Gottesman, Quantum Error Correction and Fault-Tolerance, quant-ph/0507174 (Encyclopaedia article)
  • Preskill, Fault-tolerant quantum computation, quant-ph/9712048
  • Preskill, Reliable Quantum Computers, quant-ph/9705031

Exercises

Exercises can be discussed in a tutorial after the lecture.

1. Sheet #01 (13.05.; due 20.05.)

Contact

Géza Giedke, MPQ B1.25, Tel. 089/32905-203.