Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron

Claudia Artiaco, Federico Balducci, Giorgio Parisi, Antonello Scardicchio

Published 2020-03-02Version 1

In this paper we analyze the quantum dynamics of the perceptron model, where a particle is constrained on a $(N-1)$-dimensional sphere, subjected to a set of $M=\alpha N$ randomly placed hard-wall potentials. This model has several applications, ranging from learning protocols to the effective description of the dynamics of an ensemble of hard spheres in Euclidean space in $d\to\infty$ dimensions. We find that the quantum critical point at $\alpha=2$ does not show the mean-field exponents of the classical model, which points to a non-trivial critical quantum theory. We also find that the physics of such a quantum critical point is not confined to the low-temperature region. Our findings have implications for the theory of glasses at ultra-low temperatures and for the study of quantum machine-learning algorithms.