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

Abstract

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.

Figures (9)

• Figure 1: Particular dynamical behavior emerging in our quantum brain model, starting from different initial states with different perceptage of excited neuronal qubits corresponding from top to bottom to $100\%,80\%,60\%,53\%.$ Panel (A) correspond to $\gamma=1$ and (B) to $\gamma=0.9$ respectively. Other parameters were $g_0=2$ and $\tau_r=0.$
• Figure 2: Time evolution of the number of excited neuronal qubits $1/2+\langle J_z\rangle/N$ and synaptic efficiency $r(t)$ for (left) $N=10$, and (right) $N=80$ neuronal qubits. Initial state: around half of the neuronal qubits are excited. Other parameters were $\gamma=1,$$g_0=0.05$ and $\tau_r=1.$
• Figure 3: Time evolution of the number of excited neuronal qubits $1/2+\langle J_z\rangle/N$ and synaptic efficiency $r(t)$ for (left) $N=10$, and (right) $N=80$ neuronal qubits. Initial state: no neuronal qubit is excited. Other parameters were $\gamma=1,$$g_0=0.05$ and $\tau_r=1.$
• Figure 4: Time evolution of the number of excited neuronal qubits $1/2+\langle J_z\rangle/N$ and synaptic efficiency $r(t)$ for (left) $N=10$, and (right) $N=80$ neuronal qubits. Initial state:all neuronal qubits are excited. Other parameters were $\gamma=1,$$g_0=0.05$ and $\tau_r=1.$
• Figure 5: Time evolution of the fidelity neuronal qubits for an initial state with (left) no neuronal qubits excited or all the neuronal qubits excited, (right) around half of the neuronal qubits excited ($N/2-1$), with parameters $N=80$.$\gamma=1$, initial sypatic efficacy $r_0=1$, $U=0.5$