Optimal storage capacity of quantum Hopfield neural networks

Bödeker, Lukas; Fiorelli, Eliana; Müller, Markus

doi:10.1103/physrevresearch.5.023074

Cited by 2 publications

(2 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To give an example of the use of our result, we apply it to quantum generalizations of Hopfield-like associative-memory dynamics [44]. These are recently receiving attention [45][46][47] also due to the investigation of their possible realization in multi-modal cavity setups [48][49][50][51]. More in general, our results are of interest for the physical scenarios where a collective representation of the master equation can be employed, ranging from quantumoptical settings to superradiant atomic ensembles [18,[48][49][50][52][53][54][55].…”

Section: Introductionmentioning

confidence: 92%

See 1 more Smart Citation

Quantum fluctuation dynamics of open quantum systems with collective operator-valued rates, and applications to Hopfield-like networks

Fiorelli

2024

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the dissipation features local transitions that depend on collective, operator-valued rates, encoding average properties of the system. These types of generators can be formally obtained by generalizing, to the quantum realm, classical (mean-field) stochastic Markov dynamics, with state-dependent transitions. Focusing on the dynamics emerging in the limit of infinitely large systems, we build on the exactness of the mean-field equations for the dynamics of average operators. In this framework, we derive the dynamics of quantum fluctuation operators, that can be used in turn to understand the fate of quantum correlations in the system. We then apply our results to quantum generalized Hopfield associative memories. Here we show that, asymptotically and at the description level of quantum fluctuations, only a very weak amount of quantum correlations, in the form of quantum discord, emerges beyond classical correlations.

show abstract

Section: Introductionmentioning

confidence: 92%

“…, wit h f(•) a generic function. We also employed the substitution ω t (σ α i ) = ξ µ i o µ α (t), assuming a homogeneous distribution of the misalignment between patterns and spins [46,70,79]…”

Section: Data Availability Statementmentioning

confidence: 99%