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

```python
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