| 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:
- Measure population activity (⟨σᶻ⟩)
- Adjust coupling strength J based on deviation from set point
- 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
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
