L1 - Lecturer: Pierre Rouchon
Title: An introduction to Stochastic Master Equation (SME) and feedback for open quantum systems
Outline:
1) SME of the photon box: wave-function/density-operator formulation, dispersive/resonant propagator, Markov model, quantum Monte-Carlo trajectories, (super)-matringales, Quantum Non Demolition (QND) measurement of photons, Bayesian inference to include measurement imperfections and decoherence, simulation and convergence analysis.
2) Structure of dynamical models describing open quantum systems including measurement back-action and decoherence: discrete-time models based on quantum channels and left stochastic matrices; continuous-time models driven by Wiener processes (weak measurement) and Poisson processes (quantum jump and counting measurement).
3) Feedback issues relying on classical controllers (optimizing QND measurement via Markovian feedback, quantum state stabilization via Bayesian feedback) and on quantum controllers (stabilization of Schrödinger cats via autonomous feedback).
L2- Lecturer: Vedika Khemani
L3 - Lecturer: Benjamin Huard
Title: Quantum trajectories and measurement-based feedback control of superconducting circuits
Outline:
1) Introduction to quantum superconducting circuits: resonators, qubits, readout methods
2) Measurement apparatus and their modeling: amplifiers, homodyne and heterodyne measurements, photon detectors, photon counters, quantum efficiency
3) Quantum trajectories of superconducting qubits and cavities: quantum jumps, diffusive trajectories using dispersive measurement and/or fluorescence, past quantum states approach
4) Measurement-based feedback: stabilization of qubit states and trajectories, stabilization of cavity states, use of neural networks, pros and cons of feedback control compared to reservoir engineering techniques, applications
L4 - Lecturer: Howard Wiseman
L5 - Lecturer: Klaus Molmer
L6 - Lecturer: Ion Nechita
Title: Tensor norms for quantum entanglement
A brief abstract: After introducing the basic notions about tensors, I will discuss different aspects of quantum entanglement in the framework of tensor norms. I will show how this point of view can bring new insights to this fundamental notion of quantum theory and how new entanglement criteria can be naturally obtained in this way.
Outline:
Lecture 1. Tensor products of normed spaces. From matrix to tensor norms.
Lecture 2. Entanglement of pure and mixed quantum states.
Lecture 3. Entanglement criteria from tensor norms.
L7 - Lecturer: Nina Amini