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Dekohärenz und Quantenfehlerkorrektur


The seminar takes place Mondays 10:15 AM in room 4.18 of building E2.6.

Schedule:

29.4.19: The Bloch equation - Frank Wilhelm-Mauch
6.5.19: The Lindblad equation - Yannik Weber
13.5.19 (FWM away): Quantum Channels and the Kraus decomposition: Kevin Pack
20.5.19: QEC1: Shor codes: Nicolas Wittler
27.5.19: QEC2: Stabilizer codes I: Aditi Misra
3.6.19: QEC3: Surface code: David Headley
17.6.19: QEC2: Stabilizer codes II: Aditi Misra
24.6.19: Spin echo+Dynamical decoupling: Federico Roy
1.7.19: Redfield theory: Andrii Sokolov
8.7.19: Decoherence-Free subspaces: Frank Wilhelm-Mauch
15.7.19: Caldeira Leggett: Peter Schuhmacher


Dozenten:
Frank Wilhelm-Mauch
Andrii Sokolov

Quantum coherence in realistic systems ist limited - linear superpositions of basis states decay based on interaction with the environment and ultimately find thermal equilibrium. When realising quantum technologies, this decoherence is often detrimental. Addressing this problem thus helps not only to understand the transition from quantum physics into the classical world  but also is central for realizing quantum devices. In quantum computers, the elaborate methods of quantum error correction allows to actively remove errors from the computer provided that the native error rate is not too high.

Suggested topics:

The Bloch equation
Literature: Breuer / Petruccione; Slichter
Need to cover: Density matrices, Definition of the equation, T_1 and T_2 and their measurement, spin locking and decoherence in the rotating frame, Rabi and Ramsey,

Spin Echo
Redfield theory
Literature: K. Blum „Density matrix theory“, Breuer / Petruccione, „Superconducting
Qubits II: Decoherence"
Need to cover: Derivation of the Redfield equation, Born and Markov approximations, secular approximation, expressions for T_1 and T_2 through noise spectra

The Lindblad equation
Literature: Breuer / Petruccione; Alicki / Lendi; Nielsen / Chuang
Need to cover: Quantum semigroups and divisibility, Gorini-Kossakowski-Sudarshan equation, Lindblad form, Lindblad operators for important phenomena

Dissipative phase transitions and the Caldeira-Leggett Model
Literature: Leggett et al. Rev. Mod. Phys; U. Weiss book
Need to cover: The Spin-Boson Hamiltonian and its justification, Lamb shift, effective tunnel matrix element, adiabatic renormalization, observations of the phase transition

Quantum channels and the Kraus decomposition
Literature: Breuer / Petruccione; Nielsen / Chuang
Need to cover: Definitions of quantum channels, difference between positivity and complete positivity, popular choices of Kraus operators, Choi matrices

Quantum error correction 1: Shor Codes
Literature: Nielsen / Chuang; Lidar / Brun
Need to cover: Syndrome qubits, encoding, syndrome measurement, recovery operation, threshold

Quantum error correction 2: Stabilizer formalism and CSS codes
Literature: Nielsen / Chuang; Lidar / Brun
Need to cover: Stabilizer codes, code distance, transversal gates, Gottesman-Knill theorem

Quantum error correction 3: The surface code
Literature: Lidar / Brun; Fowler et al. Paper
Need to cover: description of surface code stabilizazion, description of fault tolerant gates

Error mitigation: Spin echo and dynamical decoupling
Literature: Lidar, de Sousa, Biercuk
Need to cover: Composite pulses, CPMG seqence, filter function formalism

Decoherence-free subspaces
Literature: Whaley review
Need to cover: Definition and conditions, encoded universality

Quantum trajectories and quantum feedback
Literature: Jacobs and Steck
Need to cover: Stochastic Schrödinger equation, quantum trajectories
Schrödinger cat codes
Literature: Yale group, TBD


This is a seminar, driven by student presentations. It is suitable for students of both physics and computer science (with some talk topics being more suitable than others).

If you are interested, please contact Frank Wilhelm-Mauch, fwm-AT-lusi.uni-sb.de
A short preparation meeting will be held on April 11, 3:45 PM, E2.6 Room E.04 - we will also fix the final time there