Degrees incorporating this pedagocial element :

### Description

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