Quantum associative memory with a single driven-dissipative nonlinear oscillator

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.

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Cited by in corpus (12)

• Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator
• Dissipative phase transitions in $n$-photon driven quantum nonlinear resonators
• Time Crystal in a Single-mode Nonlinear Cavity
• Unravelling Metastable Markovian Open Quantum Systems
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• Liouvillian skin effect in quantum neural networks
• Dissipative Quantum Hopfield Network: A numerical analysis
• Stabilization of cat-state manifolds using nonlinear reservoir engineering
• Neural networks with quantum states of light
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