Clarify the relationship between classical and quantum capacity scalings

Determine whether the matching capacity exponents of the quantum dimer associative-memory Hamiltonians and classical p-spin Hopfield Hamiltonians reflect a fundamental connection between the two model classes or are merely coincidental.

Background

The paper derives a capacity scaling of order N{2p_q-1} for the p_q-th-order quantum dimer Hamiltonian and compares it with the classical p_c-spin Hopfield scaling of order N{p_c-1}. Identifying 2p_q with p_c makes the powers of system size coincide.

Although this correspondence is observed in the scaling analysis, the paper does not establish an underlying mapping, universality principle, or other theoretical explanation. The authors explicitly leave unresolved whether the agreement signals a deeper relationship between classical and quantum associative-memory models.

References

Curiously, despite qualitative differences between quantum and classical models, the capacity of the quantum model scales as the same power of the system size as the classical model simply by identifying $2p_q$ with $p_c$. Whether this is just a coincidence or indicates a deeper connection between the classical and quantum models is not yet clear.

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