arXiv:2609.28726

Associative Memory for Quantum Entangled States

Qiyuan Hu, Kartiek Agarwal, Ivar Martin

quant-phcond-mat.stat-mechSubmitted Sep 23, 2026• Announced Sep 25, 2026• 0 citations

Abstract

We generalize the canonical Hopfield model of associative memory, which stores classical states of individual spins, to store entangled quantum states. The construction is based on truncated projector-sum Hamiltonian, and we explicitly consider a special case that stores dimer singlet coverings of a spin-1/2 system. We analyze the stability of the stored memories and find that the capacity -- the number of stable patterns -- scales faster with the system size than one would expect from a naive analogy with the standard Hopfield model, suggesting a possible quantum advantage.

Comments: 15 pages, 6 figures

Related papers

Optimal storage capacity of quantum Hopfield neural networks

Lukas Bödeker, Eliana Fiorelli, Markus Müller

Quantum neural networks form one pillar of the emergent field of quantum machine learning. Here quantum generalizations of classical networks realizing associative memories---capable of retrieving patterns, or memories, from corrupted initial states---have been proposed. It is a challenging open problem to analyze quantum associative memories with an extensive number of patterns and to determine the maximal number of patterns the quantum networks can reliably store, i.e., their storage capacity. In this work, we propose and explore a general method for evaluating the maximal storage capacity of quantum neural network models. By generalizing what is known as Gardner's approach in the classical realm, we exploit the theory of classical spin glasses for deriving the optimal storage capacity of quantum networks with quenched pattern variables. As an example, we apply our method to an open-system quantum associative memory formed of interacting spin-1/2 particles realizing coupled artificial neurons. The system undergoes a Markovian time evolution resulting from a dissipative retrieval dynamics that competes with a coherent quantum dynamics. We map out the nonequilibrium phase diagram and study the effect of temperature and Hamiltonian dynamics on the storage capacity. Our method opens an avenue for a systematic characterization of the storage capacity of quantum associative memories.

arXiv:2210.07894Physical Review ResearchMay 1, 202310 citations

Quantum-stabilized patterns in a vector Hopfield network

Richard D. Barney, Sharba Bhattacharjee, Victor Galitski +2 more

We introduce the quantum vector Hopfield network, in which patterns are formed by orientations of quantum vector spins; quantum dynamics arise intrinsically from the non-commutativity of the spin operators. We derive the equations of state and the phase diagrams for this network as well as its classical counterpart. We find that quantum fluctuations, surprisingly, stabilize the stored patterns. Both the critical retrieval temperature and the target pattern overlap are enhanced relative to the classical network. Additionally, we find that this enhancement grows with pattern loading up to network capacity. We interpret this effect as an analog of quantum order-by-disorder, a mechanism by which quantum fluctuations promote the formation of ordered phases. These findings offer a new route to quantum-enhanced associative memory.

quant-pharXiv:2606.06597Jun 8, 20260 citations

High-Capacity Quantum Associative Memories

M. C. Diamantini, Carlo A. Trugenberger

We review our models of quantum associative memories that represent the “quantization” of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model with pattern-dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in Hamming distance, resulting in a high probability of measuring a memory pattern very similar to the input. The unitary operator implementing this transformation can be formulated as a sequence of one-qubit and two-qubit elementary quantum gates and is thus the exponential of an ordered quantum Ising model with sequential operations and with pattern-dependent interactions, exactly as in the classical case. Probabilistic quantum memories, that make use of postselection of the measurement result of control qubits, overcome the famed linear storage limitation of their classical counterparts because they permit to completely eliminate crosstalk and spurious memories. The number of control qubits plays the role of an inverse fictitious temperature. The accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits. These models thus solve the capacity shortage problem of classical associative memories, providing a polynomial improvement in capacity. The price to pay is the probabilistic nature of information retrieval.

arXiv:1506.01231Journal of Applied Mathematics and PhysicsJan 1, 20168 citations

Comparing Classical Hopfield Networks and a Hybrid Quantum-Classical Associative Memory Model: Recall Accuracy, Noise Robustness, and Storage Capacity

Sanjay Shivaganesh

Associative memory, the ability to reconstruct complete information from partial or noisy cues, is a defining feature of human cognition and an enduring objective in artificial intelligence. Classical neural models such as Hopfield networks have long provided insight into distributed storage and retrieval mechanisms, yet they remain constrained by limited storage capacity and susceptibility to noise. Recent developments in quantum computing have motivated investigation of hybrid quantum-classical architectures as alternative approaches to memory representation and retrieval. This study examines how effectively hybrid quantum-classical models can reproduce associative memory functions compared to Hopfield networks, with a particular focus on recall accuracy under varying noise levels, storage capacity, and computational efficiency. Through small-scale experiments using binary patterns and hybrid quantum circuits, we evaluate potential quantum advantages and practical trade-offs. The findings contribute to ongoing discourse in quantum machine learning and cognitive modeling, underscoring both the promise and current limitations of quantum-inspired associative memory systems. Our guiding research question is: To what extent can hybrid quantum–classical models replicate associative memory functions more effectively than classical neural memory models, particularly in terms of recall accuracy under noise and storage capacity?

Sep 14, 20260 citations

Quantum associative memory based on entanglement

YU Xiao-min

An approach to constructing an artificial quantum associative memory based on entanglement (QuEAM) is discussed. The QuEAM is an exponential increase in the capacity of the memory when compared to classical associative memories such as the Hopfield network. According to the characteristics of amount of entanglement, the study algorithm based on Grover's well-known algorithm is locally magnified the probability amplitude for the qubit. The basic principle of entangled states is discussed. Concrete examples illustrating the properties of the proposed model are also presented.

Chinese Journal of Quantum ElectronicsJan 1, 20051 citation

Artificial Associative Memory Using Quantum Processes

Dan A. Ventura

Abstract This paper discusses an approach to constructing an artificial quantum associative memory (QuAM). The QuAM makes use of two quantum computational algorithms, one for pattern storage and the other for pattern recall. The result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the Hopfield network. Further, the paper argues for considering pattern recall as a non-unitary process and demonstrates the utility of non-unitary operators for improving the pattern recall performance of the QuAM. 1.

Jan 1, 199812 citations