mobiu-q 1.8.6

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q (v1.8.6)

Hybrid Soft-Algebra Optimizer for Quantum Computing

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.

---

🚀 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:

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

Where $\Delta_t$ represents the dual signal $(a_t, b_t)$. This allows the "Cloud Brain" to adjust the learning rate dynamically based on algebraic trust rather than just historical averages.

** 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.

---

📊 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	+49.12%	100/100
LiH Molecule	+44.87%	100/100
Transverse Ising	+22.25%	100/100
Heisenberg XXZ	+23.01%	99/100
MaxCut	+40.50%	54/60
Vertex Cover	+39.59%	54/60
Max Independent Set	+28.85%	50/60
TOTAL AVERAGE	+35.45%	557/580

> 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.

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

---

📦 Installation

pip install mobiu-q

---

⚡ Quick Start

1. VQE (Chemistry)

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

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.

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
)

---

🔑 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

---

❓ 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.

---

Support

• Documentation: pypi.org/project/mobiu-q
• Email: [e-mail]

---

Proprietary technology. All rights reserved by Mobiu Technologies.