Quantum Hopfield Model with Dilute Memories

TL;DR

This paper analyzes the quantum Hopfield model with dilute memories, exploring its phase transition and implications for quantum annealing efficiency in spin glass systems.

Contribution

It introduces the quantum Hopfield model with dilute memories and calculates critical exponents relevant for quantum annealing.

Findings

Identifies a quantum phase transition at a critical transverse field.

Calculates critical exponents for the phase transition.

Discusses implications for quantum annealing in spin glass models.

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.