Criticality and fragility in a quantum neural memory

We theoretically investigate a neural transverse-field Hopfield (NTFH) model that realizes a minimal quantum neural memory by encoding patterns in the low-energy spectrum and stationary correlations of coupled qubits. At the level of a two-neuron open quantum system, we analyze how entanglement of formation, geometric quantum discord and quantum-memory-assisted entropic uncertainty evolve under the combined action of memory interactions, transverse fields, local imperfections and Markovian dephasing. This reveals a robust trade-off: transverse driving enhances coherent processing but destabilizes stored patterns, while local asymmetries and noise rapidly erase quantum correlations. Extending the model to a four-neuron network, we show that entanglement fluctuations peak at a transverse-field-driven quantum phase transition between a memory-ordered and a paramagnetic phase, thereby linking the fragility of quantum neural memory to standard notions of quantum criticality.