Quantum associative memory with a single driven-dissipative nonlinear oscillator

TL;DR

This paper introduces a quantum associative memory model using a single driven-dissipative nonlinear oscillator, leveraging its phase space degrees of freedom to enhance storage capacity and pattern discrimination.

Contribution

It presents a novel quantum associative memory scheme with a single oscillator, demonstrating improved capacity and tunable pattern recognition through spectral gap analysis.

Findings

Successful discrimination between multiple coherent states

Enhanced storage capacity compared to discrete neuron systems

Memory performance linked to spectral gap in Liouvillian

Abstract

Algorithms for associative memory typically rely on a network of many connected units. The prototypical example is the Hopfield model, whose generalizations to the quantum realm are mainly based on open quantum Ising models. We propose a realization of associative memory with a single driven-dissipative quantum oscillator exploiting its infinite degrees of freedom in phase space. The model can improve the storage capacity of discrete neuron-based systems in a large regime and we prove successful state discrimination between $n$ coherent states, which represent the stored patterns of the system. These can be tuned continuously by modifying the driving strength, constituting a modified learning rule. We show that the associative-memory capacity is inherently related to the existence of a spectral gap in the Liouvillian superoperator, which results in a large timescale separation in the dynamics corresponding to a metastable phase.