Mini-course: Quantum expander graphs
Cécilia Lancien (Université de Toulouse)
Abstract: The goal of this lecture is to understand what quantum expander graphs are, what they are useful for, and how they can be constructed. We will first recall the definition of classical expander graphs, and explain how quantum analogues of these objects can be defined. We will then show that, both classically and quantumly, random constructions provide with high probability examples of expander graphs. In the quantum case, such result is derived from a spectral analysis for random matrix models with a tensor product structure. The presentation will be based, among others, on:
-Random unitaries give quantum expanders. M.B.Hastings. 2007.
- Quantum expanders and geometry of operator spaces. G.Pisier. 2014
- Correlation length in random MPS and PEPS. C.Lancien and D.Peréz-García. 2019.
- Characterizing expansion, classicaly and quantumly. C.Lancien. 2020.
statistical mechanicsmathematical physicsprobability
Audience: researchers in the topic
Series comments: Description: Monthly seminar on random matrices and random graphs
| Organizers: | Guillaume Barraquand*, Laure Dumaz |
| *contact for this listing |