Quantum associative memory with a single driven-dissipative non-linear oscillator

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.