Séminaire du LPTMS: V. Bapst


11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405
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On the Quantum Annealing of Quantum Mean-Field Models

Victor Bapst, LPT ENS

In this talk I will present analytical results on the quantum annealing of quantum mean-field models. I will first explain the connection between static and dynamic properties of the model using results obtained on a toy model, the fully-connected ferromagnetic p-spin model. For p=2 this corresponds to the quantum Curie-Weiss model which exhibits a second-order phase transition, while for p>2 the transition is first order. Focusing on the latter case, I will detail the link between phase transitions, metastable states and residual excitation energy on both finite and divergent time-scales. Then, I will present a study of the thermodynamics of a more realistic optimization problem subject to quantum fluctuations: the quantum coloring problem on random regular graphs. Using the quantum cavity method, that allows to solve such models in the thermodynamic limit, we determined the order of the quantum phase transition that occurs when the transverse field is varied and unveiled the rich structure of the quantum spin-glass phase. In particular, I will explain why the quantum adiabatic algorithm would fail to solve typical instances of this problem efficiently because of entropy induced crossings within the quantum spin-glass phase.

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