Abstract
We introduce a near-term experimental platform for realizing an associative memory. It can simultaneously store many memories by using spinful bosons coupled to a degenerate multimode optical cavity. The associative memory is realized by a confocal cavity QED neural network, with the cavity modes serving as the synapses, connecting a network of superradiant atomic spin ensembles, which serve as the neurons. Memories are encoded in the connectivity matrix between the spins, and can be accessed through the input and output of patterns of light. Each aspect of the scheme is based on recently demonstrated technology using a confocal cavity and Bose-condensed atoms. Our scheme has two conceptually novel elements. First, it introduces a new form of random spin system that interpolates between a ferromagnetic and a spin-glass regime as a physical parameter is tuned---the positions of ensembles within the cavity. Second, and more importantly, the spins relax via deterministic steepest-descent dynamics, rather than Glauber dynamics. We show that this nonequilibrium quantum-optical scheme has significant advantages for associative memory over Glauber dynamics: These dynamics can enhance the network's ability to store and recall memories beyond that of the standard Hopfield model. Surprisingly, the cavity QED dynamics can retrieve memories even when the system is in the spin glass phase. Thus, the experimental platform provides a novel physical instantiation of associative memories and spin glasses as well as provides an unusual form of relaxational dynamics that is conducive to memory recall even in regimes where it was thought to be impossible.
Highlights
Five hundred million years of vertebrate brain evolution have produced biological information-processing architectures so powerful that emulating them, in the form of artificial neural networks, has led to breakthroughs in classical computing [1,2]
The associative memory is realized by a confocal cavity QED neural network, with the modes serving as the synapses, connecting a network of superradiant atomic spin ensembles,which serve as the neurons
We present an initial step along this path by theoretically showing how a network composed of atomic spins coupled by photons in a multimode cavity can naturally realize associative memory, which is a prototypical brainlike function of neural networks
Summary
Five hundred million years of vertebrate brain evolution have produced biological information-processing architectures so powerful that emulating them, in the form of artificial neural networks, has led to breakthroughs in classical computing [1,2]. Physical systems capable of realizing an Ising spin glass may play such a role In this spirit, we present a thorough theoretical investigation of a quantum-optics-based heuristic neural-network optimization solver in the context of the associative memory problem. (1) Superradiant scattering of photons by sufficiently large ensembles of atomic spins plus cavity dissipation naturally realizes a form of zero-temperature dynamics in a physical setting: discrete steepest descent (SD) dynamics. This dynamics occurs because the bath structure dictates that large energy-lowering spin flips occur most rapidly. Appendixes A–F present the following: Appendix A, the Raman coupling scheme and effective Hamiltonian; Appendix B, the derivation of the confocal connectivity; Appendix C, the derivation of the confocal connectivity probability distribution; Appendix D, the spin-flip dynamics in the presence of a classical bath with an Ohmic noise spectrum; Appendix E, the derivation of the spin-flip rate and dynamics in the presence of a quantum bath; and Appendix F, the derivation of the mean-field ensemble dynamics
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