# Mobiu-Q (v2.0)

**Universal Physics-Aware Optimizer for Stochastic Systems**

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**Mobiu-Q** is the first optimizer based on **Soft Algebra**. By mathematically decomposing gradients into *Potential* ($a_t$) and *Realization* ($b_t$), it filters out noise in real-time.

Originally designed for Quantum Computing, Mobiu-Q v2.0 is now validated for **FinTech Risk Modeling**, **Reinforcement Learning**, and **Complex Engineering** problems.

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## 🚀 The Core Innovation: "Noise Hallucination" Prevention

Standard optimizers (Adam, SGD) assume that lower objective values always indicate better solutions. In noisy environments—like NISQ processors or stochastic financial markets—this fails. Optimizers "tunnel" into noise, creating **Noise Hallucinations** (non-physical solutions).

**The Solution:**
Mobiu-Q utilizes a cross-coupled state evolution law:
```math
S_{t+1} = (\gamma \cdot S_t) \cdot \Delta_t + \Delta_t

```

This ensures that a parameter update is only committed if the *Potential Field* () is validated by a *Realized Improvement* ().

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## 🏆 Universal Benchmarks (v2.0)

Validated across **24 distinct problem domains** with 1,000+ random seeds.

| Domain | Problem | Improvement (vs Adam) | Significance |
| --- | --- | --- | --- |
| **💰 Finance** | **Credit Risk (VaR)** | **+52.3%** | Superior stability in high-volatility noise |
| **💰 Finance** | **Portfolio Opt** | **+51.7%** | Better Sharpe ratio convergence |
| **🤖 AI / RL** | **LunarLander** | **+129.7%** | 96% Win rate vs Adam's crashing |
| **📐 Classical** | **Rosenbrock Valley** | **+75.8%** | Navigates narrow, curved valleys |
| **⚛️ Quantum** | **H2 Molecule** | **+49.1%** | Chemical accuracy in noisy simulations |
| **🌀 Topology** | **SSH Model** | **+61.0%** | Identifies topological phases |
| **🕸️ Graph** | **MaxCut (QAOA)** | **+21.5%** | Escapes local minima via  |

### Hardware Verification (IBM Fez)

Tested on IBM's 127-qubit *Fez* processor:

* **Adam:** Diverged to -1.68 Ha (Noise Hallucination).
* **Mobiu-Q:** Stabilized exactly at the physical ground state (-1.176 Ha).

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## 📦 Installation

```bash
pip install mobiu-q

```

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## ⚡ Quick Start

### 1. Universal Stochastic Optimization (Finance / AI)

For noisy classical problems (Credit Risk, RL, Engineering).

```python
from mobiu_q import MobiuAPI

# Initialize Cloud Brain
opt = MobiuAPI(
    license_key="YOUR-KEY",
    problem="vqe",        # Use 'vqe' logic for stable descent
    mode="noisy",         # Activates Trust Ratio for noise filtering
    base_lr=0.05          # Standard stochastic LR
)

# Your Training Loop
for step in range(100):
    # 1. Get noisy metric (e.g., VaR, Loss, Reward)
    loss = model.evaluate(params)
    grads = model.gradient(params)
    
    # 2. Step with Noise Filtering
    params = opt.step(params, grads, loss)

```

### 2. Rugged Landscapes (Combinatorial / QAOA)

For problems with many local minima (MaxCut, Rastrigin, Ackley).

```python
opt = MobiuAPI(
    license_key="YOUR-KEY",
    problem="qaoa",       # Activates Super-Equation (Delta-Dagger)
    mode="standard",
    base_lr=0.1           # Higher kinetic energy to escape wells
)

```

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## 🔑 Pricing

* **Free Tier:** For students & testing (Limited runs).
* **Pro Tier:** Unlimited runs, Priority Processing, FinTech/AI models.

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

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