Parcours Quantum information and quantum engineering 2e année

Teacher : Pr. Alain Joye, Institut Fourier, UGA

Objectives : 
Introduce the mathematical formalism and concepts required to address the main physical questions raised in the description of open quantum systems. These lectures and tutorials will provide advanced theoretical tools to understand and model quantum open systems (quantum systems coupled to a dissipative environment), with constant opening on foundational questions of quantum mechanics, e.g. the famous “measurement problem”.

Organisation : Total of 24 hours of Lectures & Exercise classes

Program : 

Chapter 1)

* Mathematical framework, Functional Calculus for matrices
* Quantum formalism, Density matrices, Pure states, Gibbs states
* Von Neumann entropy, relative entropy and their properties
* Variational characterisation of Gibbs states
* Quantum trajectories, two-time measurement protocols

Chapter 2)

* By-partite systems, tensor products, partial traces
* Purifications, Schmidt decomposition, Entropy (in-)equalities
* Subadditivity of entropy and Landauer's bound

Chapter 3)

* Markovian approximation of Quantum Dynamics
* CPTP maps and Markovian semi-groups
* Lindblad generators and their properties
* Entropy production

Prerequisites:

Quantum Mechanics M1 

Statistical physics M1

References: 

Exploring the quantum (Haroche & Raimond, Cambridge University Press)

Quantum measurement and control (Wiseman & Milburn, Cambridge University Press)

Quantum computation (Online lectures by John Preskill)

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Teachers : Julien Claudon (CEA) and Cyril Branciard (CNRS)

Objectives :
These lectures are aimed to provide building blocks to understand and model the elementary components of light (photons), light matter-interaction at the single photon level, and elements of quantum communication and information processing with single photons.

Program :

Chapter 1: Julien Claudon (16h)
1. Quantification of the free radiation field - Photons
2. Representation of quantum states in phase space
Tutorial: Coherent states
3. Interference in quantum optics, single-photon states and wave-particle duality
4. Light-matter interaction in free space, optical Bloch equations
5. Cavity quantum electrodynamics

Chapter 2: Cyril Branciard (8h)
Entanglement, Bell’s inequalities.
Quantum cryptography (BB84, Ekert protocol), quantum teleportation.
Quantum repeaters, entanglement distribution, quantum networks.

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Teacher : Hermann Sellier (UGA)

Ojectives :
The lecture "Quantum Condensed Matter" provides a theoretical understanding of important quantum effects in solid state systems, including the quantum transport properties of electrons in metals and semiconductors, the macroscopic quantum coherence of superconductivity, and the topological properties of specific band structures.

Program :

Chapter 1: Mesoscopic physics :
- scattering process (electrons, phonons, spin, temperature dependence)
- interference effects (Aharonov-Bohm oscillations, weak localization, spin-orbit interaction)
- ballistic transport (1D conductance, quantum point contacts, quantum Hall effect)
- scattering theory (Landauer-Büttiker formalism, symmetry relations, shot noise)
- quantum dots (level spectrum, Coulomb blockade, stability diagram)

Chapter 2: Superconductivity :
- attractive interaction and Cooper pairing
- BCS theory and excitation spectrum
- order parameter and coherence length
- critical field and vortices
- Cooper pair tunneling in Josephson junctions

Chapter 3: Topological phases :
- topological invariants, spinors, Berry phase
- 1D SSH model, Kitaev chain, Majorana modes
- 2D systems, Dirac fermions, graphene, Klein tunneling
- quantum Hall effect, Chern numbers, conductance quantization

Bibliography for the lessons and tutorials :

Introduction to mesoscopic physics - Yoseph Imry - 1997 (first edition) 2002 (second edition)
Electronic transport in mesoscopic systems - Supriyo Datta  - 1995 (printed) 2013 (numeric)
Quantum transport, introduction to nanoscience - Yuli Nazarov - 2009 (printed) 2012 (numeric)
Electronic quantum transport in mesoscopic semiconductor structures - Thomas Ihn - 2004 (printed and numeric)
Introduction to superconductivity - Michael Tinkham - 1975 (first edition) 1996 (second edition) 2004 (reprint)

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Teachers : Nicolas Roch (CNRS), Tristan Meunier (CNRS and Quobly)

Objectives :
This course will present an introduction to quantum information using experimental devices. It will expose the main tools and concepts of quantum circuits and their implementation using Solid state Qubits.

Program :

Introduction : Overview of the different types of Qubits (atoms, photons and solid states)

Chapter 1: Superconducting Qubits
- Hamiltonian of an experimental circuit
- Qubit manipulation
- Circuit quantum electrodynamics and measurements.
- Decoherence processes
- Multi-Qubits

Chapter 2: Spin Qubits
- Semiconducting spin Qubits and their Hamiltonians
- Single and double dot Qubits
- Manipulation of Spin Qubits

Prerequisites:
Quantum mechanics M1, Solid state physics M1, Semiconductor physics M1

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Teachers : Hélène Béa (UGA) Vincent Baltz (CEA)

Objectives :

This lecture is an introduction to the field of nanomagnetism, also providing basic ideas in spin electronics. The continuous progress in patterning, instrumentation and simulation over the past decades has made possible the investigation of low-dimensional magnetic elements such as thin films and nanostructures. New properties arise in these due to the reduction of dimensionality and the ability to built artificial stackings. Beyond the development of fundamental knowledge, these bring new functionalities of interest for technology. Such is the case for Giant Magneto-Resistance, an effect combining together electronics and magnetism, as the resistance of a stacked device may strongly depend on the arrangement of magnetization in the sub-stacks. It was discovered in the mid 80's and led to the Nobel prize in Physics in 2007, and enters many applications such as magnetic sensors and encoders, data storage and processing, bio- and heath devices. Grenoble has played an active role in the development and magnetism from fundamentals to permanent magnets and currently spin electronics. Several large laboratories and research teams are devoted to these, with links to companies in Information/Communication technology or Health / Biology.

The lecture remains mostly at the phenomenological and materials level, and does not cover fundamental aspects of magnetism related to quantum mechanics and magnetism in compounds. The first chapter provides general notions about magnetism such as fields and moments, units and magnetostatics. The second chapter focuses on ground-state effects arising when the dimensions of a magnetic system are reduced, either as a thin film or nanostructure. These properties differ from those known at the macro scale, and thus must be taken into consideration when designing systems with nanometer dimensions. The third chapter pertains to magnetization processes, which means how a system reacts against a magnetic field. This aspect is crucial, as it determines how one is able to address a material or device. The fourth chapter considers high-speed magnetization processes, which happen to involve precessional processes. This aspect is crucial for current developments in spintronics for data storage and processing, where GHz operation may be required. Finally the fifth chapter will shortly present the basic phenomena arising coupling electronic transport and magnetism, both in terms of magnetoresistance (the arrangement of magnetization affects the resistance of a device) and magnetization actuation through spin-polarized transport (for example, programming a magnetic cell through a current flowing directly through the cell).

Program : 

 Chapter 1 : Reminders on magnetism

1. Magnetic induction, Maxwell equations and their consequences
2. Magnetic induction vs magnetic field
3. Magnetic materials
4. Units in magnetism
5. Magnetic energies
6.  Bloch domain wall
7. Magnetometry and magnetic imaging

Chapter 2 : Magnetism and magnetic domains in low dimensions

1. Magnetic ordering in low dimensions
2. Magnetic anisotropies in low dimensions
3. Domains and domain walls in thin films
4. Domains and domain walls in nanostructures

Chapter 3 : Magnetization reversal

1.  Macrospin, uniform magnetization
2. Magnetization reversal in nanostructures
3. Magnetization reversal in extended systems (thin films)

Chapter 4 : Precessional dynamics of magnetization

1. Ferromagnetic resonance and Landau-Lifshitz-Gilbert equation

2. Precessionnal switching of macrospin by magnetic field

3. Precessionnal motion of domain walls by magnetic field

4. Extra-torques in the presence of current: impact on precession

Chapter 5 : Spintronics and beyond

1. Brief overview of the field of spintronics and its applications
2. First notions to describe electron and spin transport - CIP-GMR, AMR
3. Spin accumulation - CPP-GMR
4. Transfer of angular momentum - STT
5. Berry curvature, parity and time symmetries - QHE, AHE
6. Brief non-exhaustive introduction to current topics
7. Exercices - AMR, ISHE

Bibliography :

Solid state physics textbook (Ashcroft/Mermin, Kittel,…)
Magnetism: Fundamentals (I), Tremolet de Lacheisserie (2004)
Magnetism and Magnetic Materials, J. M. D. Coey (2010)
Nanomagnetism and spintronics, T. Shinjo (2009)
Lecture notes of Olivier Fruchart
The basics of electron transport in spintronics, EDP Sciences, V. Baltz (2023)

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Teacher : Benoit Vermersch (UGA)

Objectives :

While the mathematical basis of quantum computing, the programming model, and most quantum algorithms have been published decades ago (starting in the 1990s), they have been of interest only to a small dedicated community. Time has come to make quantum algorithms and their implementations accessible to a broader audience aiming to explain the principles of quantum programming, which are quite different from those of classical programming. During these lessons and tutorials, you will learn Quantum Algorithms.

Program :

Lecture 1: From classical computers to quantum computers
- Classical computers in the circuit representation: Bits, gates, universality, computational complexity
- Motivations to build a quantum computer: Quantum parallelism and quantum speedup
- Introduction of quantum computing in the quantum circuit model
- Universal set of quantum gates – connection to entanglement
- The measurement   

Lecture 2: Quantum Algorithms  
- Warm-up: Deutsch's problem  
- Data search: Grover’s algorithm
- Factorization: Shor’s algorithm   

Lecture 3: Quantum Error correction
- The role of decoherence in a quantum circuit
- Introduction to repetition codes
- Stabilizer formalism.
- Quantum threshold theorem and fault-tolerant quantum computing. The example of surface codes   

Lecture 4: Quantum optimization I: Quantum annealing
- Warm-up: Quantum adiabatic theorem
- Quantum annealing
- Fundamental limitations of quantum annealing  

Lecture 5 : Quantum optimization II: hybrid classical quantum Quantum annealing
- Quantum approximation optimization algorithm (QAOA)
- Analog/Digital quantum Simulation.
- Solving quantum chemistry problems
– variational quantum eigensolver (VQE)   

Lecture 6 : Bonus lecture
- Implementing a quantum oracle for Grover's algoritm
- Google's quantum supremacy and toric code experiments

Useful references:  J. Preskill’s notes on quantum information: http://theory.caltech.edu/~preskill/ph229/ Quantum computation and quantum information, M. Nielsen, I. Chuang, Cambrige Press  

Prerequisite: Quantum mechanics M1

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Part I Nanofabrication in research labs:

Yannick Le Tiec (CEA) Franck Bassani (CEA) Philippe Rodriguez (CEA)

This part will cover the main nanofabrication and characterization techniques used in clean-rooms in research laboratory and semi-industrial environments for the fabrication of current and future semiconductor devices. The principles of these techniques will be presented and illustrated through concrete examples obtained in the clean-rooms of the Minatech Campus in Grenoble. This course will provide you with the basics of technological steps, thin film deposition techniques, lithography processes, and advanced characterization used during the fabrication of single devices up to their large-scale integration.

Content :

• Substrates/Materials (Si / Ge / SiGe / SOI / sSOI / Si28 / III-V….)
• Surface preparation (Batch / Single Wafer – Baths / Sprays / Cryogenics /…)
• Thin film deposition of semiconductors, insulators and metals (PVD / CVD / ECD /…
• Lithography (Photo / E-beam / Imprint) and etching (Wet / Dry) processes
• Ion implantation
• Chemical Mechanical polishing
• Molecular bonding (Wafer to Wafer / Hybrid bonding / Die to wafer / ….)
• Characterisation techniques (SPM / SEM-EDX / XRF / Ellipsometry / XPS / XRF / PL / Raman / XRD / …)

Part II : VLSI nanofabrication processes :

Maud Vinet (Quobly)

This second part describes the devices that are currently used and developed to sustain Moore’s law: it spans the transistor technologies from bulk, to Finfet and FDSOI with their pros and cons and how they are manufactured, with a quick overview of the semiconductor industry players. It also describes the evolution of Moore’s law and how it has moved from transistor to memory centric after having hit the limits of scaling, we have switched from dimensions scaling only to the introduction of new computing paradigms such as in memory computing to sustain the performance improvement of integrated circuits. Finally, it screens all the devices that are developed in order to overcome scaled transistors limitations with a strong emphasis on silicium spin qubits seen as a major contender to enable quantum computing.

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Teachers : Xavier Jehl (CEA) for Chapter 1, Hélène Jacquinot (CEA Leti) for Chapter 2

Objectives :

Key Enabling Technologies are necessary for Quantum Technologies. This course will introduce two main technological tools widely used in quantum engineering technologies but also used in micro-electronics and telecoms.

Program :

Chapter 1 : Cryoelectronics and Low temperature techniques
- Low temperature apparatus (4K and mK refrigerators)
- Electronic devices working at cryogenic temperatures
- Very low noise devices (Josephson parametric amplifier), cryo-CMOS.g.

Chapter 2 : RF/Microwave techniques
- Microwave propagation
- Classical communication systems and modulations
- Transceivers characteristics, heterodyne and homodyne architecture

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This UE Thematic and interdisciplinary projects is divided in 2 parts :

Part 1 : Quantum practicals on IBM-Q
Teachers : Julien Renard (CNRS) Matias Urdampilleta (CNRS)

Projects will be focused on the implementation of elementary quantum algorithms on superconducting quantum processors and simulators (IBM-Q). It relies on a “learning by doing” strategy. Developed skills: Python & quantum circuits.

Part 2 : Quantum seminars

A series of seminars (regular and extended ones) will complete the regular course offer during the fall semester.
For the academic year 2024-2025, the program (18 hours in total) is the following:

• 3 extended seminars (3 x 1.5 hours each)
  - Mechanical systems in the quantum limit, Jérémie Viennot (CNRS)
  - Spin Qubits with NV centers, Benjamin Pigeau (CNRS)
  - Modeling and Simulation for Spin Quantum Dots and Qubits, Yann-Michel Niquet (CEA)

• 3 regular seminars (1.5 hour each)

            - What is a PhD ? Olivier Isnard, Director of the Physics Doctoral School
            - Quantum Start-ups presentations.
            - Short presentations of PhDs students about their work.

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Your Master Thesis can be done in a research laboratory, an industry or a startup, in Grenoble, in France, or in another country. The minimum length for your internship has to be 4 months, and the maximum 6 months.

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