Basic quantum mechanics: Hilbert space, observables, Hermitian operators, the Schrödinger representation, the Heisenberg representation, the interaction representation, the Schrödinger equation, the measurement problem, entanglement, Einstein's 'spooky action at a distance' impact.

Quantum information handling: local operations and classical communication, quantum key distribution, various quantum calculation infrastructures.

Dynamics of open quantum systems in general. Time evolution of partial density matrices. Kraus operators.

Quantum-Markov processes. The Lindblad equation and Lindblad operators.

Decoherence and dissipation. Quality measures.

General dynamics of open quantum systems: The Feynman-Vernon functional.

Real sources of error in quantum calculation components. The Aharonov-Kitaev-Nisan model for error propagation.

The Jaynes-Cumming model and the spin-boson model.

Simulation techniques for open quantum systems with memory.

After passing the course, the student shall be able to

• use basic theoretical and numerical methods to describe quantum systems interacting with an environment
• give an account of how performance and limitations of quantum information systems and components depend on the properties and interference from a quantum mechanical environment
• evaluate and design quantum information components

in order to

• in an independent and scientifically substantiated way, be able to understand and appreciate the influence of the environment on mainly quantum information processing systems, but also on quantum technology more generally
• be able to assess what is possible and not possible to do with a given quantum calculation platform.

Quantum information handling: local operations and classical communication, quantum key distribution, various quantum calculation infrastructures.

Dynamics of open quantum systems in general. Time evolution of partial density matrices. Kraus operators.

Quantum-Markov processes. The Lindblad equation and Lindblad operators.

Decoherence and dissipation. Quality measures.

General dynamics of open quantum systems: The Feynman-Vernon functional.

Real sources of error in quantum calculation components. The Aharonov-Kitaev-Nisan model for error propagation.

The Jaynes-Cumming model and the spin-boson model.

Simulation techniques for open quantum systems with memory.

Schedule (2023)

The schedule will be given here when it will have been decided by the KTH scheduling service. All lectures will be in study period 1, academic year 2023-2024.

Additional material (2023) [suggested additional reading]

On the general representation of open quantum systems dynamics, as an alternative to the course book (Breuer & Petruccione) Section 2.4.3 "Representation theorem for quantum operations", one can also read 

   Ingemar Bengtsson & Karol Życzkowski
   Geometry of Quantum states (First ed.)
   Cambridge University Press (2016)
   Section 10:3

Similar material can also be found in 

   On Duality between Quantum Maps and Quantum States
   Karol Życzkowski & Ingemar Bengtsson
   Open Systems & Information Dynamics volume 11, pages3–42 (2004)
   https://link.springer.com/article/10.1023/B:OPSY.0000024753.05661.c2

The Feynman-Vernon theory is in the course presented following the original paper

  R.P Feynman & F.L. Vernon Jr
  The theory of a general quantum system interacting with a linear dissipative system
  Annals of Physics, vol 24, pages 118-173 (1963)
  https://www.sciencedirect.com/science/article/pii/000349166390068X

The original paper contains valuable material on symmetry properties and a priori results which are not covered in the course book. For a system interacting with a bath of harmonic oscillators the general form of the influence functional depends on two kernels, these days most often written and k_i and k_r. These kernels are not derived in the MSc course as this is too lengthy on this level. For those students who want to see a derivation a possible source is :

   Erik Aurell, Ryochi Kawai & Ketan Goyal
   An operator derivation of the Feynman–Vernon theory, with applications to the generating function of bath energy changes and to an-harmonic baths
   J. Phys. A: Math. Theor. 53 275303 (2020)
   https://iopscience.iop.org/article/10.1088/1751-8121/ab9274/meta

The Theory of Open Quantum Systems
  Heinz-Peter Breuer och Francesco Petruccione
  Oxford University 2007  
  DOI:10.1093/acprof:oso/9780199213900.001.0001

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

A, B, C, D, E, FX, F

• HEM1 - Home work, 7.5 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Grade A is examined through an oral examination.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.