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arXiv:2009.01227 · Physical Review X

Enhancing Associative Memory Recall and Storage Capacity Using Confocal Cavity QED

Brendan Marsh, Yudan Guo, Ronen M. Kroeze, Sarang Gopalakrishnan, Surya Ganguli, Jonathan Keeling, Benjamin Lev

Published Jun 2, 2021• 61 citations

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 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.

DOI: 10.1103/physrevx.11.021048

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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 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.

The Hopfield neural network stores memories using all-to-all-coupled spins and recalls those memories through equilibrium dynamics. Storing too many hampers recall because frustration causes an exponential number of spurious patterns to arise as the network becomes a spin glass. Despite this, we show that memory recall can be restored, and even enhanced, under quantum-optical nonequilibrium dynamics that convert spurious patterns into reliable memories. We experimentally observe associative memory with high storage capacity in a driven-dissipative spin glass made of atoms and photons. The capacity surpasses that of the Hopfield model under Hebbian learning by up to sevenfold in a 16-spin network. Atomic motion boosts capacity by dynamically modifying connectivity akin to short-term synaptic plasticity in neural networks, realizing a precursor to learning in a quantum-optical system.

Models of interacting complex systems provide the fundamental statistical physics reference frame for the study and the understanding of associative memories, machine learning, and the dynamics of neural networks. On the other hand, simulating complex multi-synaptic interactions on a classical hardware is computationally demanding due to the super-linear scaling of the system complexity. Photonic quantum technologies provide a promising solution to these limitations by leveraging on their inherent speed and parallel processing ability in order to simulate complex networks. Recently, a connection between multiphoton processes and generalized

p

-body Hopfield models has been theoretically established. Here, we design and demonstrate an experimental platform that exploits single photons distributed across a set of optical modes, in which controlled arrays of binary phase shifters act as Ising-like neurons. We focus specifically on a fully connected Hopfield Hamiltonian with four-body local interaction terms, realized via two-photon processes. Through quantum simulations on programmable photonic processors, the study identifies three distinct regimes: a memory retrieval phase, a spin-glass memory "black-out" phase, and a paramagnetic phase. Experimental results confirm successful memory retrieval at low storage capacities and temperatures, where the system consistently relaxes to fixed points with high memory overlap, effectively reconstructing the stored patterns. Future research will extend the platform design to investigate networks with local or dilute interactions, while advances in the realization of scalable photonic circuits will enable architectures that encompass very large numbers of interacting spins.

We present a novel cavity QED system in which a Bose–Einstein condensate (BEC) is trapped within a high-finesse optical cavity whose length may be adjusted to access both single-mode and multimode configurations. We demonstrate the coupling of an atomic ensemble to the cavity in both configurations and measure that the single-atom, -mode cooperativity exceeds unity. The atoms are confined either within an intracavity far-off-resonance optical dipole trap or a crossed optical dipole trap via transversely oriented lasers. Multimode cavity QED provides fully emergent and dynamical optical lattices for intracavity BECs, in that the process of atomic self-organization may be described as a continuous symmetry breaking phase transition resulting in the emergence of a compliant lattice with phonon-like excitations. Such systems will enable explorations of quantum soft matter, including superfluid smectics, superfluid glasses, and spin glasses as well as neuromorphic associative memory.

We realize a driven-dissipative Ising spin glass using cavity QED in a novel "4/7" multimode geometry. Gases of ultracold atoms trapped within the cavity by optical tweezers serve as effective spins. They are coupled via randomly signed, all-to-all Ising cavity-mediated interactions. Networks of up to n=25 spins are holographically imaged via cavity emission. The system is driven through a frustrated transverse-field Ising transition, and we show that the entropy of the spin glass states depends on the rate at which the transition is crossed. Despite being intrinsically nonequilibrium, the system exhibits phenomena associated with Parisi's theory of equilibrium spin glasses, namely, replica symmetry breaking (RSB) and ultrametric structure. For system sizes up to n=16, we measure the Parisi function q(x), Edwards-Anderson overlap q_{EA}, and ultrametricity K correlator; all indicate a deeply ordered spin glass under RSB. The system can serve as an associative memory and enable aging and rejuvenation studies in driven-dissipative spin glasses at the microscopic level.

In the present Letter, we introduce, develop, and investigate a connection between multiphoton quantum interference, a core element of emerging photonic quantum technologies, and Hopfield-like Hamiltonians of classical neural networks, the paradigmatic models for associative memory and machine learning in systems of artificial intelligence. Specifically, we show that combining a system composed of N_{ph} indistinguishable photons in superposition over M field modes, a controlled array of M binary phase shifters, and a linear-optical interferometer, yields output photon statistics described by means of a p-body Hopfield Hamiltonian of M Ising-like neurons ±1, with p=2N_{ph}. We investigate in detail the generalized four-body Hopfield model obtained through this procedure, undergoing a transition from a memory retrieval to a memory black-out regime, i.e., a spin-glass phase, as the amount of stored memory increases. The mapping enables novel routes to the realization and investigation of disordered and complex classical systems via efficient photonic quantum simulators and describes aspects of structured photonic systems in terms of classical spin Hamiltonians.

Photons in multimode optical cavities can be used to mediate tailored interactions between atoms confined in the cavities. For atoms possessing multiple internal (i.e., “spin”) states, the spin–spin interactions mediated by the cavity are analogous in structure to the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between localized spins in metals. Thus, in particular, it is possible to use atoms in cavities to realize models of frustrated and/or disordered spin systems, including models that can be mapped on to the Hopfield network model and related models of associative memory. We explain how this realization of models of associative memory comes about and discuss ways in which the properties of these models can be probed in a cavity-based setting.