Lecture series on Quantum Engineering at University Paris-Saclay

Optical quantum engineering, from fundamentals to applications

Philippe GRANGIER (Laboratoire Charles Fabry, IOGS, Palaiseau)

In this course we will start from basic quantum mechanics and introduce progressively qubits, entanglement, and Bell's inequalities; some details will be given about « Aspect's experiments » realized in the 1980's at Institut d'Optique, as well as on the recent « loophole free Bell tests » realized in 2015. In the second part we will point out the links between entanglement, quantum measurement, and quantum gates, and illustrate these ideas using some simple examples. In the third and fourth parts these ideas will be applied to quantum optics experiments with Gaussian and non Gaussian states, quantum cryptography, and possible future quantum networks.

Lecture 1 (7 March, 9:15-10:45) : Qubits, entanglement and Bell’s inequalities.

Lecture 2 (14 March,11:00-12:30) : Entanglement in a Quantum Measurement Process : from QND measurements to quantum gates.

Lecture 3 (21 March, 9:15-10:45) : Quantum optics with discrete and continuous variables

Lecture 4 (28 March, 11:00-12:30) : Quantum cryptography and optical quantum networks

 

Related material:
* Cohen Tannoudji, Diu et Laloé, Mécanique Quantique
* Bases on Quantum Information: Nielsen et Chuang; lecture notes by John Preskill, published but also available on-line
* Classical information theory (Shannon etc) : book by de Cover et Thomas

Electrical quantum engineering with superconducting circuits

Patrice BERTET and Reinier HEERES (Service de Physique de l’Etat Condensé, CEA-Saclay)

The research field of quantum state engineering with electrical superconducting circuits was born from fundamental questionings about the possibility of observing macroscopic quantum phenomena. This led to the experimental demonstration, 15 years ago, that the quantum state of an electrical circuit can be manipulated and read-out. Superconducting circuits based on Josephson junctions can thus behave as genuine artificial two-level atoms, which can be used as quantum bits. Compared to real atoms, these superconducting qubits are macroscopic in size, leading to large electrical or magnetic dipole, which facilitates their coupling to other circuits. Superconducting qubits can in particular be strongly coupled to superconducting resonators. This coupled qubit-resonator system is described by the Jaynes-Cummings model, which also describes the coupling of real atoms to high-quality-factor resonators in Cavity Quantum Electrodynamics (QED). The circuit version (called by analogy to atomic physics « Circuit QED ») offers an architecture for quantum information processing since it enables qubit readout and multi-qubit entanglement and gates. Recent experiments have demonstrated the operation of elementary quantum processors based on up to 10 qubits. In addition, it is possible to couple superconducting circuits and resonators to other quantum systems such as spins or mechanical resonators, forming socalled Hybrid Quantum Devices.

Lecture 1 (7 March, 11:00-12:30; P. Bertet) : Introduction to superconducting circuits and qubits

Lecture 2 (14 March, 9:15-10:45; R. Heeres) : Circuit QED : qubit state readout, and resonator quantum state engineering

Lecture 3 (21 March, 11:00-12:30; P. Bertet) : Multi-qubit quantum state engineering and quantum gates

Lecture 4 (28 March, 9:15-10:45; P. Bertet): Introduction to Hybrid Quantum Devices

Related Material:

• lecture notes of David Mermin
• lecture notes by John Preskill, see above.

The NV Color Centre in Diamond: Physics and Applications

Jean-François ROCH (Laboratoire Aimé Cotton, ENS Paris-Saclay, Univ Paris-Sud and CNRS, Orsay)

The NV color centre in diamond was identified in 1965 as a luminescent defect with an electron spin S=1. It then received a lot of attention after the discovery in 1997 that this point defect can be isolated as an individual quantum system inside the solid state matrix. Its remarkably stable photoluminescence even at room luminescence makes this system an efficient and practical singlephoton source. Its electron spin can be addressed and coherently manipulated using a combination of optical and microwave excitations. The understanding of the NV centre physical properties, in parallel with remarkable progresses in diamond material fabrication, has now led to many applications in sensing and quantum information which this series of four lectures will try to review.

Lecture 1 (27 September, 9:15-10:45) : The NV centre: Spectroscopy and energy levels

Lecture 2 (4 October, 11:00-12:30) : The electron spin of the NV centre

Lecture 3 (18 October, 9:15-10:45) : Magnetometry and other sensing applications using the NV centre

Lecture 4 (25 October, 11:00-12:30) : Nuclear spins in diamond as a quantum ressource

Quantum optics of many-body systems

Igor MEKHOV (CEA-Saclay, St. Petersburg State University, University of Oxford)

Both quantum optics and physics of many-body strongly correlated systems are recognized fundamental bases for developing quantum technologies. Novel paradigms arise at the intersection of several fields such as atomic and condensed matter physics. I will briefly review some ideas, where the many-body aspects of quantum systems provide key advantages over a collection of singleparticle elements. Then, I will present approaches to reach regimes, where not only the quantization of light and matter are equally important, but the quantum nature of the measurement process and dissipation plays a central role as well.

Lecture 1 (27 September, 11:00-12:30) : Quantum optics of light waves and quantum waves of ultracold matter

Lecture 2 (4 October, 9:15-10:45) : Many-body systems for quantum simulations and metrology

Lecture 3 (18 October, 11:00-12:30) : Quantum nature of the measurement process and dissipation

Lecture 4 (25 October, 9:15-10:45) : Merging quantizations of light and matter, perspectives for quantum engineering

 

Introduction to Quantum Computing

Anthony LEVERRIER and Mazyar MIRRAHIMI (Inria Paris)

In 1994, Peter Shor took the computer science community by surprise by devising an efficient algorithm for factoring that could run on a quantum computer. This was a totally unexpected discovery since the difficulty of factoring large integers is at the basis of most cryptosystems deployed today on the internet.
In this course, we will provide an introduction to quantum computing and review the main quantum algorithms, in particular Shor’s algorithm for factoring and Grover’s algorithm for searching in a database.
Building a large scale quantum computer capable of implementing such algorithms for real world data has turned out to be an extremely challenging project, due to the issue of decoherence. In a second part of the course, we will discuss approaches to fight decoherence, namely quantum error correction and quantum fault-tolerance

29 May, 5 June, 18 June and 25 June 2018 2018:

 

Nanofabrication techniques

Dominique Mailly (C2N)

29 May, 18 June and 25 June 2018:

 

Topological insulators and geometrical band theory

Jean-Noël Fuchs (LPTMC, Jussieu)

8, 15, 22 and 22 January 2019

We will start by recalling some mathematical notions of topology by using historical examples in physics : topological defects in order parameters (notion of homotopy groups) and the Dirac magnetic monopole (notion of fiber bundles). Then, we will present geometrical band theory (i.e., Berry phases for Bloch electrons in crystals) and the integer quantum Hall effect (i.e., the Chern number also known as the Thouless-Kohmoto-Nightingale-den Nijs invariant) as a first example of a topological insulator. Next, we will study gaphene in order to introduce Dirac fermions as possible excitations in condensed matter. From the massless case (gapless graphene), we will turn to the massive case (gapped graphene) by opening a gap in different ways : (1) via an inversion symmetry breaking (boron nitride, “trivial” Dirac insulator, quantum valley Hall effect) ; (2) via time-reversal symmetry breaking (Haldane’s model, Chern topological insulator, anomalous quantum Hall effect) ; and (3) via a spin-orbit coupling that breaks no symmetry of the graphene layer (model of Kane and Mele, Z2 topological insulator, quantum spin Hall insulator).

Entangled structures in classical and quantum optics

Antonio Zelaquett-Khoury (Universidade Federal Fluminense, Niterói, RJ, Brasil)

8, 15, 22 and 22 January 2019

Lecture 1: Optical vortices as entangled structures in classical optics

In this lecture we introduce the paraxial wave equation that describes the propagation of collimated optical beams and the corresponding solutions in terms of orthonormal mode functions of the beam transverse coordinates. When combined with polarization, they give rise to a tensor product vector space of spin-orbit modes where non-separable (entangled) structures can be recognized as the well-known vector beams.
 
Lecture 2: Quantum-like simulations and the role of quantum inequalities

Quite surprisingly, these entangled structures can be used to simulate some quantum information protocols. Moreover, the spin-orbit mode entanglement can be evidenced by quantum-like inequalities. We will present experimental investigations on both aspects of this classical-quantum connection in optics.
 
Lecture 3: Quantization of the electromagnetic field

In this lecture we introduce the basics of the electromagnetic field quantization and present the quantum field description under different mode decompositions. A special attention will be given to the paraxial modes mentioned in Lecture 1. Different quantum states will be discussed such as Fock, coherent and squeezed states. The corresponding transformations implied by different mode structures will be presented.
 
Lecture 4: Vector beam quantization and the unified framework

In this last lecture we present the quantized vector beams and discuss the interplay between quantum and classical entanglement in the quantized field framework. Coherent and Fock states provide elementary examples illustrating the subtle connections between mode separability and quantum entanglement.