An introduction to quantum cryptography, computation and error correction.
Course of the Physics Department

Pierre Rouchon
Mines ParisTech, PSL Research University - Quantic Research Team, Inria

Tuesday, October 23, 2018
4:00 p.m. — room conf IV (24 rue Lhomond)

These two introductory lectures present some key features motivating the construction of quantum cryptosystems and computers. They also explain some major limitations due to error and decoherence. Even for the popular physical platforms based on super- conducting qubits (illustrated by the above photo of a quantum circuit from Martinis group at UCSB/Google) the development of quantum error correction schemes adapted to the physical contraints remains an open issue.

Title of lecture 1. Quantum cryptography and computation motivated by classical cryptography schemes.
After a rapid description of classical public-key cryptography schemes, we explain
- how quantum computations with the Shor’s algorithm based on the quantum Fourier transform can break such classical public-key cryptography schemes ;
- how quantum cryptography with the BB84 protocol allows unconditionally secure transmission.

These explanations rely on fundamental quantum features underlying multi-qubits, quantum gates and circuits, no-cloning theorem and measurement processes.

Title of lecture 2. Quantum error correction with a quantum feedback perspective. Firstly, we present the three-qubit bit-flip and phase-flip codes and explain
- how the Shor code (concatenation of bit-flip and phase-flip codes) protects against the effects of an arbitrary error on a single qubit ;
- how quantum error correction relies on quantum non demolition measurement and feedback stabilization.
Secondly, we focus on two actual developments to cope with continuous-time aspects that are neglected in the above usual discrete-time setting :
- measurement-based feedback stabilization of the code-space with diffusive syndrome measurement.
- coherent feedback stabilization underlying the cat code exploiting multi-photon driven dissipative processes.

PNG - 87.5 ko