PH6604: Introduction to Open Quantum Systems
Syllabus
Module 1: Preliminaries
Lecture hours: 5 · Tutorial hours: 0 · Lab hours: 0
Pure states and statistical mixture of quantum states, Density matrix formalism, Schrödinger equation, Composite quantum systems, Quantum entropy and quantum measurement .
Module 2: Open quantum systems with Kraus operator formalism
Lecture hours: 16 · Tutorial hours: 0 · Lab hours: 0
Representation, Schrödinger equation as a special case, Complete positivity and quantum maps, Perspectives from quantum information theory, Quantum maps of a qubit as examples, unital maps, Phase-damping, bit-flip, depolarizing, and amplitude-damping maps, Idea of errors in quantum protocols .
Module 3: Quantum master equation
Lecture hours: 16 · Tutorial hours: 0 · Lab hours: 0
Lindblad equation from Born, Markov, and rotating-wave approximations, From Kraus operators to the Lindblad equation via a short time expansion of quantum maps, Lindblad equation and completely positive map, Examples with phase-damping and amplitude-damping/spontaneous emission of a single qubit .
Module 4: Introduction to non-Markovian quantum processes
Lecture hours: 5 · Tutorial hours: 0 · Lab hours: 0
Nakajima-Zwanzig equation, From Nakajima-Zwanzig to Born master equation .
Study Materials
Textbooks
- The Theory of Open Quantum Systems, H. P. Breuer and F. Petruccione, Oxford University Press, ISBN: 0-19-852063-8
- Open Quantum Systems: An Introduction, A. Rivas and S. Huelga, Springer Berlin, Heidelberg, ISBN: 978-3-642-23354-8
- Quantum Computation and Quantum Information, M. A. Nielsen and I. L. Chuang, Cambridge University Press (2007), ISBN: 978-81-7596-092-3
References
- Lecture Notes by John Preskill, Caltech, John Preskill, https://www.preskill.caltech.edu/ph229/
- Introduction to the Theory of Open Quantum Systems, Piotr Szańkowski, SciPost Physics Lecture Notes, https://scipost.org/SciPostPhysLectNotes.68