Simple Glass Models and their Quantum Annealing

Thomas Jorg 1, Florent Krzakala 2, Jorge Kurchan 3, A. C. Maggs 2

Physical Review Letters 101 (2008) 147204

We study first order quantum phase transitions in mean-field spin glasses. We solve the quantum Random Energy Model using elementary methods and show that at the transition the eigenstate suddenly projects onto the unperturbed ground state and that the gap between the lowest states is exponentially small in the system size. We argue that this is a generic feature of all `Random First Order' models, which includes benchmarks such as random satisfiability. We introduce a two-time instanton to calculate this gap in general, and discuss the consequences for quantum annealing.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Laboratoire de Physico-Chimie Théorique (LPCT),
    CNRS : UMR7083 – ESPCI ParisTech
  • 3. Physique et mécanique des milieux hétérogenes (PMMH),
    CNRS : UMR7636 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – ESPCI ParisTech