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Multiphoton Quantum Simulation of the Generalized Hopfield Memory Model.

Gennaro Zanfardino1,2,3, Stefano Paesani4, Luca Leuzzi5,6

  • 1Università degli Studi di Salerno, Dipartimento di Ingegneria Industriale, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy.

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This study connects multiphoton quantum interference with classical neural networks. It shows how photonic systems can simulate complex classical models, enabling new insights into associative memory and machine learning.

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Area of Science:

  • Quantum optics and artificial intelligence.
  • Explores the intersection of quantum interference and classical neural network models.

Background:

  • Multiphoton quantum interference is key to photonic quantum technologies.
  • Hopfield-like Hamiltonians model associative memory and machine learning.

Purpose of the Study:

  • To establish a connection between multiphoton quantum interference and Hopfield-like Hamiltonians.
  • To investigate the use of photonic systems as quantum simulators for classical models.

Main Methods:

  • Utilized a system of indistinguishable photons, phase shifters, and a linear-optical interferometer.
  • Mapped output photon statistics to a p-body Hopfield Hamiltonian (p=2N_{ph}).
  • Investigated a generalized four-body Hopfield model.

Main Results:

  • Demonstrated that photonic systems can generate output statistics described by Hopfield Hamiltonians.
  • Observed a transition from memory retrieval to a spin-glass phase in the simulated model.
  • Showcased the potential for photonic quantum simulators to study complex classical systems.

Conclusions:

  • The developed mapping provides novel routes for simulating disordered classical systems using photonic quantum simulators.
  • This work bridges quantum technologies and classical artificial intelligence, offering new perspectives on both fields.