# Quantum information processing

## Summary

Information is processed in physical devices. In the quantum regime the concept of classical bit is replaced by the quantum bit. We introduce quantum principles, and then quantum communications, key distribution, quantum entropy, and spin dynamics. No prior knowledge of quantum physics is required.

## Content

**Introduction a la mecanique quantique des systemes discrets.**

- Polarization of photons, basic experiments

- Notion of quantum state, notion of measurement

- Quantum principles, notion of quantum bits, entanglement, no-cloning

- Bloch sphere**Cryptographie, Communications et Corrélations**

- Secret key generation: BB1984 and B92 protocols

- Entanglement: EPR pairs

- Bell/CSCH inequalityl. Ekert protocol for a secret key generation

- Teleportaion, dense coding, distillation.

**Spin and its dynamics**

**-** Stern-Gerlach experiment, spin 1/2

- Dynamics of spin in magnetic fields, Rabi oscillations

- Manipulations of the spin and elementary quantum gates

**Density matrices and Von Neumann entropy**

- mixed states and entropy

- bipartite systems and entanglement entropy

- non-signalling and teleportaion revisited

## Keywords

Polarization, spin, measurement, quantum bit, entanglement, key distribution, teleportaion, dense coding, Von Neumann entropy, spin dynamics.

## Learning Prerequisites

## Required courses

Linear algebra, basic probability.

## Recommended courses

Basic physics classes: classical mechanics, waves.

## Important concepts to start the course

Vectors, matrices, eigenvalues, eigenvectors, projectors, inner product, algebraic manipulation of complex numbers, discrete probability distribution.

## Learning Outcomes

By the end of the course, the student must be able to:

- Describe principles of quantum physics
- Illustrate quantum bits with photon polarization and spin
- Explain basic communication protocols like key distribution, dense coding, teleportation
- Describe how to manipulate qubits with magnetic fields
- Define quantum entropies and list basic properties
- Use IBM Q NISQ devices

## Teaching methods

Ex-Cathedra lectures, exercise session, practical implementationns typically with IBM Q machines.

## Expected student activities

Participation in class, homeworks, hands-on exercises on IBM-Q.

## Assessment methods

miniprojet, graded homeworks, final written exam

## Supervision

Office hours | No |

Assistants | Yes |

Forum | Yes |

Others | Assistants are in exercise session. |

## Resources

## Virtual desktop infrastructure (VDI)

No

## Bibliography

**David Mermin**, *Quantum computer science, An introduction, Cambridge university press 2000. *Written for computer science students with no knowledge of physics.

**Michel Le Bellac**, *A short introduction to quantum information and quantum computation,**Cambridge University Press*. A pedagogic book with an elementary introduction to the physics of the subject.

**Neil Gershenfeld**. *The physics of information technology. Cambridge University Press.* On basic information technologies useful in computer science, classical communications and quantum aspects.

## Ressources en bibliothèque

- Quantum computer science / Mermin
- A short introduction to quantum information and quantum computation / Le Bellac
- The physics of information technology / Gershenfeld

## Notes/Handbook

Yes on web site

## Websites

## In the programs

**Semester:**Fall**Exam form:**Written (winter session)**Subject examined:**Quantum information processing**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**1 Hour(s) per week x 14 weeks

**Semester:**Fall**Exam form:**Written (winter session)**Subject examined:**Quantum information processing**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**1 Hour(s) per week x 14 weeks

**Semester:**Fall**Exam form:**Written (winter session)**Subject examined:**Quantum information processing**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**1 Hour(s) per week x 14 weeks

**Semester:**Fall**Exam form:**Written (winter session)**Subject examined:**Quantum information processing**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**1 Hour(s) per week x 14 weeks