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Forthcoming: Quantum information and quantum computation (II): Applications

Goethe University, Spring 2012 [Vorlesungsverzeichnis]

Course overview:

Time and placeMo 16:00 - 18:00, Phys 2.114 
LanguageGerman
Audience students of physics, mathematics or computer science
Prerequisites quantum mechanics
Goal to discuss key applications of quantum information and quantum computation and
their experimental realisation

Recommended reading:

  • M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information,
    Cambridge University Press, 2000 [Amazon]
  • N. D. Mermin, Quantum computer science, Cambridge University Press, 2007 [Amazon]
  • A. Peres, Quantum theory: concepts and methods, Kluwer Academic Publishers, 1995 [Amazon]
  • A. Steane, Quantum Computing, Rept. Prog. Phys. 61 (1998) 117-173 [arXiv|journal]
  • J. Preskill (Caltech), Quantum Computation, lecture notes, 2008 [www]
  • U. Vazirani (U Berkeley), Quantum Computation, lecture notes, 2007 [www]
  • H. Klauck (U Frankfurt), Quantum Computing (in German), lecture notes, 2005 [www]

Syllabus (preliminary):

Part I: Important algorithms

Lecture 1introduction, course outline, recommended literature
Lecture 2quantum Fourier transform, quantum phase estimation, order-finding, factoring (Shor algorithm)
Lecture 3 quantum search algorithm, Grover iteration, quantum counting, solution of NP-complete problems,
database search

 
Part II: Experimental realisation

Lecture 4 general prerequisites, DiVincenzo criteria, harmonic oscillator, quantum computer, non-linear optical
photon quantum computer, optical cavity QED
Lecture 5 ion traps, nuclear magnetic resonance
Lecture 6 comparison of non-linear optics vs. ion traps: qubit representation, physical states, Hamiltonian,
implementation of 1-qubit and CNOT operations, initial state preparation, timing issues, readout,
typical time scales, open problems

 
Part III: Special topics

Lecture 7one-way quantum computing, adiabatic quantum computing
...(continuation to be determined)                                                                                                         



Quantum information and quantum computation (I): Foundations

Goethe University, Fall 2011/12 [Vorlesungsverzeichnis]

Course overview:

Audience students of physics, mathematics or computer science
Prerequisites quantum mechanics
Goal to introduce the main ideas and techniques of the modern field of quantum information
and quantum computation

Recommended reading:

  • M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information,
    Cambridge University Press, 2000 [Amazon]
  • N. D. Mermin, Quantum computer science, Cambridge University Press, 2007 [Amazon]
  • A. Peres, Quantum theory: concepts and methods, Kluwer Academic Publishers, 1995 [Amazon]
  • A. Steane, Quantum Computing, Rept. Prog. Phys. 61 (1998) 117-173 [arXiv|journal]
  • J. Preskill (Caltech), Quantum Computation, lecture notes, 2008 [www]
  • U. Vazirani (U Berkeley), Quantum Computation, lecture notes, 2007 [www]
  • H. Klauck (U Frankfurt), Quantum Computing (in German), lecture notes, 2005 [www]

Syllabus:

Part I: Classical theory of communication and computation

Lecture 1 course outline; classical probability, information, entropy, Shannon's noiseless channel coding theorem,
classical data compression
Lecture 2 communication in the presence of noise, channel capacity, error-correcting codes,
Shannon's noisy channel coding theorem, classical theory of computation: network model, logic gates
Lecture 3 reversible computation, Landauer's principle, Turing machine, computational complexity,
uncomputable problems

 
Part II: Fundamentals of quantum theory and quantum information

Lecture 4 review of basic principles of quantum mechanics, qubits, Bloch sphere representation,
composite systems, Schmidt decomposition
Lecture 5
(3h)		 peculiar features of quantum theory: entanglement, Bell's theorem, Kochen-Specker theorem,
quantum Zeno effect 
Lecture 6 density matrix, reduced states, purification, general measurements (POVM)
Lecture 7 quantum information: quantum entropy, Holevo bound, Schumacher's quantum noiseless
channel coding theorem

 
Part III: Quantum circuits and simple protocols

Lecture 8 general setup of quantum circuits, single-qubit gates, CNOT and controlled-U gates, universal set
of quantum gates, simple circuit identities
Lecture 9 qubit swap, no-cloning theorem, Bell states, quantum teleportation
Lecture 10dense coding, binary function gate, Deutsch's algorithm, basic idea of quantum cryptography
Lecture 11secure quantum key distribution (BB84 protocol), quantum error correction (I): 3-qubit bit flip code
Lecture 12 quantum error correction (II): Shor code, course summary & wrap-up

 

 

Probability in modern physics (II): Processes

Goethe University, Spring 2011

Course overview:

Audience students of physics
Prerequisites quantum mechanics, statistical mechanics
Goal to introduce the key concepts and techniques for the description of dynamical, communication and
computational processes; and for the transition from the microscopic to the macroscopic domain                    

Recommended reading:

  • M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information,
    Cambridge University Press, 2000 [Amazon]
  • A. Steane, Quantum Computing, Rept. Prog. Phys. 61 (1998) 117-173 [arXiv|journal]
  • R. Balian, From microphysics to macrophysics, vol. II, Springer, 1992 [Amazon]
  • E. Fick and G. Sauermann, Quantum statistics of dynamic processes, Springer, 1990
  • E. T. Jaynes, Papers on probability, statistics and statistical physics (ed. by R. D. Rosenkrantz), Kluwer, 1989 [Amazon]
  • J. Rau, Statistical mechanics in a nutshell (1998) [arXiv:physics/9805024]
  • J. Rau and B. Müller, From Reversible Quantum Microdynamics to Irreversible Quantum Transport, Physics Reports 272, 1 (1996) [doi][arXiv]

Syllabus:

Part I: Microscopic

Lecture 1 introduction, course outline, recommended literature 
Lecture 2 unitary evolution, general measurements (POVM), quantum operations, completely positive maps,
measurement-based processes, causality
Lecture 3 classical theory of communication, Shannon's noiseless channel coding theorem, classical
data compression
Lecture 4 quantum information: quantum entropy, Holevo bound, Schumacher's quantum noiseless
channel coding theorem, relationship between entropy and information
Lecture 5 qubits, Bloch sphere representation, composite systems, general setup of quantum
circuits, single-qubit gates, CNOT and controlled-U gate, simple circuit identities,
no-cloning theorem, Bell states, quantum teleportation
Lecture 6dense coding, Deutsch's algorithm, quantum cryptography, secure quantum key distribution
(BB84 protocol), quantum error correction, 3-qubit bit flip code

 
Part II: Macroscopic

Lecture 7 problem statement: the transition from reversible, linear microdynamics to dissipative and
possibly non-linear macrodynamics; Liouville equation, superoperator formalism, projectors;
example: decay of a single resonance; mean-field term, memory term, stochastic force
Lecture 8 Nakajima-Zwanzig projection technique; Kawasaki-Gunton projector, Robertson equation;
origin of dissipation, non-linearity, memory effects and effective forces; time scale analysis;
approximations: Markov approximation, quasistationary limit, perturbation theory; H theorem
Lecture 9    Example: spin coupled to external field and bosonic heat bath (Bloch equation)
Lecture 10 Example: Boltzmann equation
Lecture 11 second law of thermodynamics, approach to equilibrium; wrap-up                                                       




Probability in modern physics (I): States

Goethe University, Fall 2010/11

Course overview:

Audience students of physics
Prerequisites quantum mechanics, statistical mechanics
Goal to review the basic concepts of probability theory and discuss their central role in
fundamental theories of physics: quantum theory and statistical mechanics                           


Recommended reading:

  • D. S. Sivia and J. Skilling, Data analysis: a Bayesian tutorial, Oxford University Press, 2nd ed., 2006 [Amazon]
  • E. T. Jaynes, Probability theory: the logic of science, Cambridge University Press, 2003 [Amazon]
  • E. T. Jaynes, Papers on probability, statistics and statistical physics (ed. by R. D. Rosenkrantz), Kluwer, 1989 [Amazon]
  • J. M. Bernardo and A. F. M. Smith, Bayesian theory, Wiley, 2000 [Amazon]
  • A. Peres, Quantum theory: concepts and methods, Kluwer Academic Publishers, 1995 [Amazon]
  • M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information,
    Cambridge University Press, 2000 [Amazon]
  • J. Rau, On quantum vs. classical probability, Annals of Physics 324, 2622 (2009) [doi][arxiv]
  • R. Balian, From microphysics to macrophysics, vol. I, Springer, 1991 [Amazon]
  • J. Rau, Statistical mechanics in a nutshell (1998) [arXiv:physics/9805024]

Syllabus:

Part I: Microscopic

Lecture 1 introduction, course outline, recommended literature 
Lecture 2propositions, weak vs. strong logic, logical implication, complement, measurement, joint decidability,
atomic propositions, graphical representation
Lecture 3 examples: classical sample space, non-classical toy models, Hilbert space
Lecture 4 non-contextuality, realism, observables, Peres-Mermin square, Kochen-Specker theorem
Lecture 5 deductive logic vs. plausible reasoning, Bayesian view on probabilities, state, sum rule,
convex cone of states, pure vs. mixed states
Lecture 6examples of convex cones, Gleason theorem, projection operators, Born rule,
quantum state space; operationalism
Lecture 7 classical Bayes rule, marginalisation, quantum measurement, Lüders rule
Lecture 8 Zeno effect; composite systems, reduced density matrix, entanglement, Bell (or CHSH) inequality, 
locality, Bell theorem

 
Part II: Macroscopic

Lecture 9 quantum source, exchangeable sequences, limit theorem for conditional probabilities
Lecture 10 de Finetti representation, (meta-)Bayes rule and marginalisation for exchangeable sequences,
global state, reductionism, empiricism, informational completeness, state tomography
Lecture 11 relative entropy, quantum Stein lemma, entropy concentration theorem, typical frequency range,
examples: Wolf's die data, state tomography for qubits
Lecture 12 generic setting of macroscopic inference problem, modelling prior ignorance, effective
single-constituent state, principle of minimum relative entropy; emergence of classicality
Lecture 13 thermodynamic entropy, thermodynamic variables, first law of thermodynamics, free energy,
grand potential; homogeneity, Gibbs-Duhem relation
Lecture 14 correlations, distance and volume on state manifold; level of description, hierarchy of inference
problems, statistical significance of fluctuations, thermodynamic model selection
Lecture 15non-parametric estimation, hyperparameters, evidence procedure; wrap-up




 

Probability in modern physics (II): Processes
Goethe University, Spring 2010

Probability in modern physics (I): States
Goethe University, Fall 2009/10

Quantum information and quantum computation (II): Applications
Goethe University, Spring 2009

Quantum information and quantum computation (I): Foundations
Goethe University, Fall 2008/09

Older lectures

Transport theory, Dresden University of Technology, 1997 [www]

Elementary mathematical methods for physics, Dresden University of Technology, 1996 [www]
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