Dynamic Synaptic Modulation of LMG Qubits populations in a Bio-Inspired Quantum Brain

We present a biologically inspired quantum neural network that encodes neuronal populations as fully connected qubits governed by the Lipkin-Meshkov-Glick (LMG) quantum Hamiltonian and stabilized by a synaptic-efficacy feedback implementing activity-dependent homeostatic control. The framework links collective quantum many-body modes and attractor structure to population homeostasis and rhythmogenesis, outlining scalable computational primitives -- stable set points, controllable oscillations, and size-dependent robustness -- that position LMG-based architectures as promising blueprints for bio-inspired quantum brains on future quantum hardware.