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

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,

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

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

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

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

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

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

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

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

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

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

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

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