Quantum Hopfield Model with Dilute Memories

Abstract: We discuss adiabatic spectra and dynamics of the quantum, i.e. transverse field, Hopfield model with dilute memories (the number of stored patterns $p < log_2 N$, where $N$ is the number of qubits). At some critical transverse field the model undergoes the quantum phase transition from the ordered to the paramagnetic state. The corresponding critical exponents are calculated and used to determine efficiency of quantum annealing protocols. We also discuss implications of these results for the quantum annealing of generic spin glass models.