100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Cécilia Lancien

Quantum expander graphs
Tuesday, 5 October, 2021 - 14:00 to 15:00
Résumé : 

The goal of the talk will be 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.

Some references on which the presentation will be based: 
- Random unitaries give quantum expanders. M.B.Hastings. 2007.
- Quantum expanders and geometry of operator spaces. G.Pisier. 2014.
- On the spectral gap of random quantum channels. C-González-Guillén, M.Junge and I.Nechita. 2018.
- Correlation length in random MPS and PEPS. C.Lancien and D.Peréz-García. 2021.
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