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Probability in modern physics (II): Processes University of Frankfurt, Spring 2010 [Vorlesungsverzeichnis] Course overview: | Time and place | Mo 16:00 - 18:00, Phys 2.114 | | Language | German | | 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 | 19 Apr | introduction, course outline, recommended literature | | 26 Apr | unitary evolution, general measurements (POVM), quantum operations, completely positive maps,
measurement-based processes, causality | | 3 May | classical theory of communication, Shannon's noiseless channel coding theorem, classical
data compression | | 10 May | quantum information: quantum entropy, Holevo bound, Schumacher's quantum noiseless
channel coding theorem, relationship between entropy and information | | 17 May | 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 | | 31 May | dense coding, Deutsch's algorithm, quantum cryptography, secure quantum key distribution
(BB84 protocol), quantum error correction, 3-qubit bit flip code |
Part II: Macroscopic | 7 Jun | 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 | | 21 Jun | 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 | | 28 Jun | Example: spin coupled to external field and bosonic heat bath (Bloch equation) | | 5 Jul | Example: Boltzmann equation | | 12 Jul | second law of thermodynamics, approach to equilibrium; wrap-up |
Probability in modern physics (I): States University of Frankfurt, Fall 2009/10 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 | 12 Oct | introduction, course outline, recommended literature | | 19 Oct | propositions, weak vs. strong logic, logical implication, complement, measurement, joint decidability,
atomic propositions, graphical representation | | 26 Oct | examples: classical sample space, non-classical toy models, Hilbert space | | 2 Nov | non-contextuality, realism, observables, Peres-Mermin square, Kochen-Specker theorem | | 9 Nov | deductive logic vs. plausible reasoning, Bayesian view on probabilities, state, sum rule,
convex cone of states, pure vs. mixed states | | 16 Nov | examples of convex cones, Gleason theorem, projection operators, Born rule,
quantum state space; operationalism | | 23 Nov | classical Bayes rule, marginalisation, quantum measurement, Lüders rule | | 30 Nov | Zeno effect; composite systems, reduced density matrix, entanglement, Bell (or CHSH) inequality,
locality, Bell theorem |
Part II: Macroscopic | 7 Dec | quantum source, exchangeable sequences, limit theorem for conditional probabilities | | 14 Dec | de Finetti representation, (meta-)Bayes rule and marginalisation for exchangeable sequences,
global state, reductionism, empiricism, informational completeness, state tomography | | 11 Jan | relative entropy, quantum Stein lemma, entropy concentration theorem, typical frequency range,
examples: Wolf's die data, state tomography for qubits | | 18 Jan | generic setting of macroscopic inference problem, modelling prior ignorance, effective
single-constituent state, principle of minimum relative entropy; emergence of classicality | | 25 Jan | thermodynamic entropy, thermodynamic variables, first law of thermodynamics, free energy,
grand potential; homogeneity, Gibbs-Duhem relation | | 1 Feb | correlations, distance and volume on state manifold; level of description, hierarchy of inference
problems, statistical significance of fluctuations, thermodynamic model selection | | 8 Feb | non-parametric estimation, hyperparameters, evidence procedure; wrap-up |
Quantum information and quantum computation (II): Applications University of Frankfurt, Spring 2009 Course overview: | Audience | students of physics, mathematics or computer science | | Prerequisites | quantum mechanics | | Goal | to review briefly the basic concepts of quantum information and quantum
computation and discuss key applications 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: Part I: Review of basic concepts | 20 Apr | introduction, course outline, recommended literature | | 27 Apr | qubits, Bloch sphere representation, composite systems, general setup of quantum
circuits, single-qubit gates, CNOT and controlled-U gate, simple circuit identities | | 4 May | qubit swap, no-cloning theorem, Bell states, quantum teleportation | | 11 May | dense coding, binary function gate, Deutsch algorithm, basic idea of quantum cryptography | | 18 May | secure quantum key distribution (BB84 protocol), quantum error correction, 3-qubit bit flip code |
Part II: Important algorithms | 25 May | student presentation [Hartmann, Bauer]: quantum Fourier transform, quantum phase estimation,
order-finding, factoring (Shor algorithm) | | 8 Jun | student presentation [Aktas, Gesiarz]: quantum search algorithm, Grover iteration, quantum counting,
solution of NP-complete problems, database search |
Part III: Experimental realisation | 22 Jun | student presentation [Lange, Kompel]: general prerequisites, DiVincenzo criteria, harmonic oscillator
quantum computer, non-linear optical photon quantum computer, optical cavity QED | | 2 Jul | student presentation [Kaiser, Milanovic]: ion traps, nuclear magnetic resonance | | 6 Jul | 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 IV: Special topics | 13 Jul | one-way quantum computing, adiabatic quantum computing; course wrap-up |
Quantum information and quantum computation (I): Foundations
University of Frankfurt, Fall 2008/09 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 |
Syllabus: Part I: Classical theory of communication and computation | 13 Oct | course outline; classical probability, information, entropy | | 20 Oct | Shannon's noiseless channel coding theorem, classical data compression | | 27 Oct | communication in the presence of noise, channel capacity, error-correcting codes,
Shannon's noisy channel coding theorem | | 3 Nov | classical theory of computation: network model, logic gates, reversible computation,
Landauer's principle | | 10 Nov | Turing machine, computational complexity, uncomputable problems |
Part II: Fundamentals of quantum theory and quantum information | 17 Nov | principles of quantum mechanics, two-level systems, composite systems, Schmidt decomposition | | 24 Nov | density matrix, entanglement, purification, general measurements (POVM), quantum operations | | 1 Dec | conceptual issues of quantum theory: quantum vs. classical probability, Kochen-Specker theorem,
Bell's theorem | | 8 Dec | quantum information: quantum entropy, Holevo bound, Schumacher's quantum noiseless
channel coding theorem |
Part III: Quantum circuits and simple protocols | 26 Jan | quantum circuit model of computation, single-qubit operations, controlled operations,
universal set of quantum gates, Solovay-Kitaev theorem | | 4 Feb | no-cloning theorem, Bell states, quantum teleportation, dense coding, Deutsch's algorithm,
quantum cryptography, quantum key distribution | | 9 Feb | quantum error correction, Shor code |
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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