# Mobiu-Q (v1.7.0)

**Hybrid Soft-Algebra Optimizer for Quantum Computing**

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[![Win Rate](https://img.shields.io/badge/Win%20Rate-99.3%25-brightgreen)](https://mobiu.ai)
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Mobiu-Q is a cloud-based optimizer that uses **Soft Algebra** to accelerate quantum algorithms. It demonstrates **algorithmic superiority** in standard conditions and **extreme resilience** in noisy environments, achieving a 99.3% win rate across 1,000 benchmarks.

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## 🚀 The Problem
* **In Simulation (Standard):** Standard optimizers (Adam) often overshoot the minimum or converge slowly due to rigid momentum.
* **On Hardware (Noisy):** Shot noise causes gradients to fluctuate, trapping optimizers in false local minima.

## 💡 The Solution: Hybrid Cross-Coupling
Mobiu-Q wraps your optimization loop with a cloud-based brain that cross-validates every step using **Soft Algebra Logic**:

```math
S_{t+1} = (\gamma \cdot S_t) \cdot \Delta_t + \Delta_t
````

Where the dual multiplication `·` ensures that potential is inextricably linked to realized gain. This creates a "smarter" momentum that adapts instantly to both clean and noisy landscapes.

** Note: In v1.6+, the optimizer utilizes a decoupled Vector EMA implementation of the Soft Algebra state evolution to maximize numerical stability on noisy hardware.

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## 📊 Comprehensive Benchmarks

### 1\. Robustness & Generalization (1,000 Runs)

**Settings:** Standard Mode, LR=0.01 (Fair fight vs Adam default).
Tested across 10 different Hamiltonians, 100 seeds each.

| Problem Domain | Improvement vs Adam | Win Rate |
|----------------|---------------------|----------|
| **H2 Molecule** | **+34.5%** | 96/100 |
| **LiH Molecule** | **+28.5%** | 100/100 |
| **Transverse Ising** | **+35.8%** | 100/100 |
| **Heisenberg XXZ** | **+23.7%** | 100/100 |
| **He4 Atom** | **+29.1%** | 97/100 |
| **TOTAL AVERAGE** | **+28.7%** | **993/1000** |

*\> **Insight:** Even in standard conditions, Mobiu-Q finds deeper energy levels than Adam.*

### 2\. The "Ultimate Fair" Test (High Noise)

**Settings:** Noisy Mode, 500 Shots, CRN (Common Random Numbers).
We compared Mobiu-Q against Adam and Naive EMA under heavy quantum noise.

![Mobiu-Q Benchmark](https://mobiu.ai/wp-content/uploads/2025/12/ultimate.png?raw=true)

*Figure 1: Green (Mobiu-Q) ignores the noise floor that traps Adam (Blue) and fails Naive EMA (Orange).*

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## 📦 Installation

```bash
pip install mobiu-q
```

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## ⚡ Quick Start

### 1\. VQE (Chemistry)

Best for molecular simulations (`H2`, `LiH`, etc).

```python
from mobiu_q import MobiuQCore
import numpy as np

# Initialize Cloud Optimizer
opt = MobiuQCore(
    license_key="YOUR-LICENSE-KEY",
    problem="vqe",        # Optimized for chemistry
    mode="standard",      # Use "noisy" for real hardware
    base_lr=0.01          # Standard learning rate
)

# Your Physics Loop
params = np.random.uniform(-0.1, 0.1, n_params)

for step in range(80):
    # 1. Measure (Local)
    energy = measure_energy(params)
    gradient = calculate_gradient(params)
    
    # 2. Optimize (Cloud Brain)
    params = opt.step(params, gradient, energy)

opt.end()
```

### 2\. QAOA (Combinatorial)

Best for MaxCut, Vertex Cover, and rugged landscapes.

```python
opt = MobiuQCore(
    license_key="YOUR-LICENSE-KEY",
    problem="qaoa",       # Uses Super-Equation Δ†
    mode="noisy",         # Recommended for QAOA
    base_lr=0.1           # Aggressive learning rate
)
```

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## 🔑 Pricing & Licenses

We offer a free tier for researchers and students.

  * **Free:** 5 runs / month (No credit card required).
  * **Pro:** Unlimited runs, priority support.

**[Get your License Key Here](https://app.mobiu.ai)**

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## ❓ FAQ

**Q: Why use cloud optimization?**
A: The Soft Algebra computation requires stateful cross-coupling history that is best managed centrally. It allows us to deploy updates to the "Brain" without you needing to update your Python package.

**Q: Is my data safe?**
A: We only receive anonymous gradients and energy scalars. Your Hamiltonian / Circuit structure remains locally on your machine. We never see your IP.

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## Support

  * **Documentation:** [pypi.org/project/mobiu-q](https://pypi.org/project/mobiu-q/)
  * **Email:** ai@mobiu.ai

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*Proprietary technology. All rights reserved by Mobiu Technologies.*