Develop dynamical and dissipative retrieval of entangled memories

Develop a dynamical and dissipative formulation of the quantum associative-memory network that determines how entangled memories can be stored and retrieved in open quantum systems, rather than only analyzing static properties of closed systems.

Background

The analysis in the paper concerns static energetic stability, quantum hybridization, and eigenstate properties of closed Hamiltonian systems. It does not establish a physical retrieval protocol that dynamically reconstructs a selected entangled memory from a corrupted or partial input.

The authors state that incorporating dynamics and dissipation is necessary for practical storage and retrieval, drawing an analogy with dissipative and dynamical mechanisms used in classical and open-system Hopfield networks. The unresolved problem is therefore to formulate and analyze such a dynamical extension for entangled quantum memories.

References

Several questions remain open. First, the current model stores only a very simple kind of quantum entangled states with a valence bond structure. It would be interesting to apply our framework to accommodate other classes of entangled memories, such as random stabilizer graph states . Second, our analysis focused essentially on static properties of closed quantum systems. Including dynamics and dissipation would be necessary to study how such networks can be used in practice for storage and retrieval of entangled memories, analogous to the dynamical mechanisms employed in classical Hopfield networks . We leave these question for future investigations.

— Associative Memory for Quantum Entangled States  (2609.28726 - Hu et al., 23 Sep 2026) in Section Discussion