Lecture/QIT I WS0607

From MPQTheory

Quantum Information Theory: Implementations of Quantum Information Processing

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

Lecture: Fr 13 - 15h, Tutorial: Fr 15 - 16h,

PH 127 Garching

We discuss the basics of the main implementations of quantum information processing (QIP) in quantum optical and solid state systems. We study how qubits are defined, how quantum gates are realized, and which are the relevant decoherence processes. Examples of proposed and realized QIP protocols are analysed.

The lecture is continued in the summer term: Fr. 14:30 - 16:00, PH 227

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

Outline:

1. Introduction
   1. Motivation and historical development
   2. Elements of Quantum Information Processing
      1. States: quantum registers (pure vs. mixed; purification of a state; composite systems: tensor product; separable vs. entangled; qubits: Bloch sphere)
      2. Measurements (observable, von-Neumann measurement; generalized measurement; Pauli matrices)
      3. Time-evolution (Hamiltonians, quantum gates, single qubit unitaries)
      4. application: teleportation
   3. Quantum Circuits
      1. general operations; quantum gate array
      2. universal quantum gates
2. Elements of Quantum Optics
   1. canonical quantization, states of the radiation field
   2. light matter interaction: minimal coupling,
   3. approximations: long wavelength, dipole, rotating wave
   4. atom and a continuum of modes: master equation (Lit.: Cohen-Tannoudji, Atom-Photon interactions, ch IV; Gardiner, Quantum Noise, ch. 5.1; Breuer Open Quantum Systems)
   5. atom and a single mode: Jaynes-Cummings model: dressed states, Rabi oscillations, collapses and revivals; quantum gates, asymptotic completeness; cavity decay; (Lit.: Scully and Zubairy, Quantum Optics ch. 6; J. Kimble, Strong interactions of Single Atoms and Photons in Cavity QED Physica Scripta T76, 127 (1998); Law and Eberly, Arbitrary Control of a Quantum Electromagnetic Field, Phys. Rev. Lett. 76, 1055 (1996); Raimond et al., Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys 73, 565 (2001); Gleyzes et al., Observing the quantum jumps of light: birth and death of a photon in a cavity, quant-ph/0612031)
   6. adiabatic elimination (Lit.: Brion et al., quant-ph/0610056)
   7. mechanical effects of light (Lit.: Cohen-Tannoudji, Atom-Photon interactions, ch II.A; IV.E.2; V.C.2; Metcalf and van der Straten, Laser cooling and trapping, Springer)
3. Quantum Optical Implementations of QIP
   1. ion trap quantum computer: trapping, engineering two-qubit gate in an ion-trap, gate limitations and optimization (Lit.: D.F.V. James, Quantum Dynamics of Cold Trapped Ions, with Application to Quantum Computation, Appl. Phys. B 66, 181-190 (1998); J. I. Cirac and P. Zoller, Quantum Computations with Cold Trapped Ions, Phys. Rev. Lett. 74, 4091, (1995); J.-J. Garia-Ripoll et al., Speed Optimized Two-Qubit Gates with Laser Coherent Control Techniques for Ion Trap Quantum Computing, Phys. Rev. Lett. 91, 157901 (2003)).

Part II: begins Fr, Apr 20, 14:30 in room PH227

• • photonic qubits: teleportation and quantum communication
  • building quantum networks with cavity-QED
  • decoherence in quantum optical systems
  • optional: quantum memories: atomic ensembles
  • optional: quantum simulation in optical lattices
• solid state based approaches
• superconducting qubits
• optional: alternative approaches: linear optics QC, one-way QC, topological QC

Requirements:

Quantum Mechanics, Electrodynamics

Literature:

• Nielsen and Chuang, Quantum Information, Cambridge University Press
• Walls and Milburn, Quantum Optics, Springer; Cohen-Tannoudji, Atom-Photon Interactions, Wiley
• Cirac, Duan, and Zoller Quantum optical implementation of quantum information processing
• Coish and Loss, Quantum Computing with spins in solids
• Devoret et al., Superconducting Qubits: a short review
• European QIPC roadmap
• US Quantum Computation Roadmap

Exercises

Given by Christine Muschik, MPQ B1.42, Tel. 089/32905-315.

1. Sheet #1 (03.11.; due 10.11.)
2. Sheet #2 (10.11.; due 17.11.) Solutions
3. Sheet #3 (24.11.; due 01.12.) Solutions
4. Sheet #4 (08.12.; due 15.12.)
5. Sheet #5 (22.12.; due 11.01.) Solutions
6. Sheet #6 (26.01.; due 02.02.) (See also: PRA 55 R2489)
7. suggestions for the end-of-term presentation (for Fri, Feb 9, 2007)
   1. entanglement creation (a simple practical protocol): Cabrillo et al., Creation of entangled states of distant atoms by interference Phys. Rev. A 59, 1025 - 1033 (1999) (see Matsukevich et al., Entanglement of Remote Atomic Qubits Phys. Rev. Lett. 96, 030405 (2006) for a related experiment)
   2. entanglement distillation (how to obtain pure entangled states from noisy ones): Bennett et al., Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels, Phys. Rev. Lett. 76, 722, (1996) (related experiment: Reichle et al., Experimental purification of two-atom entanglement, Nature 443 838 (2006))
   3. long-distance quantum communication (a scalable proposal): Briegel et al., Quantum repeaters: The role of imperfect local operations in quantum communication, Phys. Rev. Lett. 81, 5932, (1998)
   4. quantum cryptography (unconditionally secure key distribution): Bennett and Brassard, Quantum cryptography: public key distribution and coin tossing, Proc. IEEE Int. Conf. on Computers, Systems, and Signal Processing p.175 (1984); see also Nielsen/Chuang, ch.12.6. See Gisin et al., Quantum cryptography Rev. Mod. Phys. 74, 145 (2002) for background and an extensive review.

... or suggest your own.

Contact:

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