Introduction to quantum computing (A. Borbely) :
The course will have the following parts :
Overview of conventional logic-gates and simple circuits (ex. half-adder and adder)
Classical probabilistic devices (coin tossing automata, concatenated gates)
The Mach-Zehnder interferometer
The postulates of quantum mechanics (a review)
Qubits and registers (Bloch sphere, manipulation of qubits in 3D)
Superposition and quantum measurement (ex. Stern & Gerlach experiment)
Evolution of a quantum system, unitary transformations
Single qubit gates (bit flip, phase flip, phase rotator, Hadamard transform)
Qubits and the uncertainty principle
Two qubits, quantum entanglement, Bell states and the Einstein-Podolsky-Rosen paradox
CHSH inequality (nonlocal correlations)
Two qubit gates
No cloning theorem, quantum teleportation
N-qubits
Grover’s quantum algorithm (finds the unique input to a black-box function that produces a particular output)
Light-matter interaction and optical systems (M. Perrin) :
We will start with a general review of the Maxwell and Helmholtz formalism, first in vacuum, or in a homogeneous medium, then in the media described by a 3D permittivity profile. Different typical cases will be presented (monochromatic beam, time / frequency regimes, paraxial approximation, dispersion relation). This will imply to understand the theoretical foundations, and the different classes of electromagnetic models, as well as their limitations. The very general notion of mode and natural frequency (in general, a complex number) will be approached, drawing examples from optical fibers, metallic nanoparticles or resonant dielectrics, planar waveguides on substrates, Bragg mirrors, etc ...
The expression of the permittivity of materials will be presented using the models of Drude, Sommerfeld, in relation to their electronic structure.
We will explain how the characteristics of the material, and the shape of the object (its symmetries) influence its properties (filtering, routing, resonant emission / absorption, dispersive propagation, polarization). Current challenges, such as the fabrication and engineering of complex systems (eg self-assembled), the race to very small scales (from micron to nano, then to sub-nano), precise measurement of g (~ 9.81 ms-2), will be presented as examples.
We will then describe the main mechanisms of electromagnetic field / matter interaction at the microscopic level (electronic / vibrational / rotational transitions) and associated spectroscopies, as well as their applications (detection of hazardous materials, fraud, chemical analysis). Finally, we will briefly explain the coupling between the equations of evolution of an atom that emits light and Maxwell's equations.
An important part will be dedicated to the study of practical applications (or systems) such as: the modeling of a laser, the study of an OLED and biological sensors (type surface plasmon sensors), in order to practice the knowledge acquired at the beginning of the course.
In particular, practical work using finite element software will allow students to numerically model real systems.
| On completion of the unit, the student will be capable of: | Classification level | Priority |
|---|---|---|
| Know the binary logic gates | 1. Knowledge | Useful |
| Better understand the basics of quantum mechanics | 2. Understand | Important |
| Understanding the quantum phenomenon "entanglement" | 2. Understand | Essential |
| Know the qubit-based logic gates | 1. Knowledge | Essential |
| Being able to evaluate a quantum circuit | 6. Assess | Essential |
| Know new ways of transmitting information (without the possibility of decryption) | 1. Knowledge | Important |
| Understand a simple quantum calculation algorithm | 2. Understand | Important |
| Master the formalism | 3. Apply | Essential |
| Understand the main types of light / matter interactions | 4. Analyse | Important |
| Model simple optical systems | 6. Assess | Useful |
| Percentage ratio of individual assessment | Percentage ratio of group assessment | ||||
|---|---|---|---|---|---|
| Written exam: | 65 | % | Project submission: | 20 | % |
| Individual oral exam: | 0 | % | Group presentation: | 0 | % |
| Individual presentation: | 7 | % | Group practical exercise: | 7 | % |
| Individual practical exercise: | 0 | % | Group report: | 0 | % |
| Individual report: | 0 | % | |||
| Other(s): 0 % | |||||
| Type of teaching activity | Content, sequencing and organisation |
|---|---|
| Course | Introduction to quantum computing : Light-matter interaction and optical systems : |
| Tutorial classes | Introduction to quantum computing : Light-matter interaction and optical systems : |
| Practical classes | Light-matter interaction and optical systems : |