dynamic-synaptic-lmg-quantum-brain

name

dynamic-synaptic-lmg-quantum-brain

description

Bio-inspired quantum neural network using Lipkin-Meshkov-Glick (LMG) Hamiltonian with synaptic-efficacy feedback for activity-dependent homeostatic control. Use when: studying quantum brain models, quantum neural networks with homeostasis, LMG Hamiltonian for neural populations, collective quantum many-body attractors, quantum rhythmogenesis, population homeostasis in qubit systems, scalable quantum computational primitives.

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

Overview

arXiv: 2602.16003 (2026)

Biologically inspired quantum neural network encoding neuronal populations as fully connected qubits governed by the LMG quantum Hamiltonian, stabilized by synaptic-efficacy feedback for activity-dependent homeostatic control.

Core Architecture

LMG Hamiltonian for Neural Populations

H_LMG = -J/N · Σᵢⱼ σᵢᶻσⱼᶻ - h · Σᵢ σᵢˣ

• Neuronal populations → fully connected qubit ensembles
• Collective quantum many-body modes → attractor structure
• Size-dependent robustness emerges naturally

Synaptic-Efficacy Feedback

Activity-dependent homeostatic control loop:

1. Measure population activity (⟨σᶻ⟩)
2. Adjust coupling strength J based on deviation from set point
3. Feedback stabilizes quantum dynamics → prevents runaway excitation

Computational Primitives

Primitive	Description
Stable set points	Homeostatically maintained activity levels
Controllable oscillations	Rhythmogenesis via feedback parameters
Size-dependent robustness	Larger populations → more stable quantum states

Implementation Pattern

1. Population Encoding

Map neural population firing rates to qubit expectation values:

firing_rate → ⟨σᶻ⟩ ∈ [-1, 1]

2. Homeostatic Feedback Loop

def update_coupling(J, activity, target, rate=0.01):
    error = activity - target
    return J - rate * error  # synaptic efficacy adjustment

3. Quantum Evolution

Evolve under time-dependent LMG Hamiltonian with feedback-adjusted parameters.

Key Insights

• LMG architecture provides natural scalability to quantum hardware
• Synaptic feedback bridges biological realism with quantum dynamics
• Attractor structure supports memory-like behavior
• Rhythmogenesis emerges from feedback parameters

Applications

• Bio-inspired quantum computing architectures
• Quantum neural network simulation on future quantum hardware
• Theoretical neuroscience with quantum formalism
• Quantum memory and rhythm generation

Activation Keywords

LMG Hamiltonian, quantum brain, bio-inspired quantum neural network, synaptic efficacy, homeostatic control, quantum many-body, attractor dynamics, rhythmogenesis, population homeostasis, qubit neural network, quantum neuroscience