mobiu-q 2.8.6

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q v2.8.6

Mobiu-Q wraps your existing optimizer with Soft Algebra to filter noise and improve convergence. Same API, better results.

---

⚡ Quick Start

from mobiu_q import MobiuOptimizer

# PyTorch (RL, LLM, Deep Learning)
base_opt = torch.optim.Adam(model.parameters(), lr=0.0003)
opt = MobiuOptimizer(base_opt, license_key="YOUR_KEY", method="adaptive")

# Quantum (VQE, QAOA) - pass params instead of optimizer
params = np.random.randn(10)
opt = MobiuOptimizer(params, license_key="YOUR_KEY", method="standard", mode="simulation")

Note: MobiuOptimizer auto-detects PyTorch optimizers vs numpy arrays and uses the appropriate backend.

---

🔧 Configuration

Methods

Method	Best For	Default LR
standard	VQE, Chemistry, smooth landscapes	0.01 (sim) / 0.02 (hw)
deep	QAOA, combinatorial, rugged landscapes	0.1
adaptive	RL, LLM, high-variance problems	0.0003

Modes (Quantum only)

Mode	When to Use	Gradient Method
simulation	Clean simulator (Qiskit Aer, PennyLane default)	Finite Difference (2N evals)
hardware	Real quantum hardware, FakeFez, noisy backends	SPSA (2 evals, noise-resilient)

Rule of thumb: If your backend has noise → use hardware. If it's a perfect simulator → use simulation.

Base Optimizers (MobiuQCore only)

Available: Adam (default), AdamW, NAdam, AMSGrad, SGD, Momentum, LAMB

Note: Optimizer names are case-sensitive!

A/B Testing Parameter

# For fair comparisons, toggle Soft Algebra:
opt = MobiuOptimizer(base_opt, use_soft_algebra=True)   # Default - SA enabled
opt = MobiuOptimizer(base_opt, use_soft_algebra=False)  # Baseline - SA disabled

---

📦 Installation

pip install mobiu-q

---

🎯 Usage Examples

PyTorch (RL / LLM / Deep Learning)

Use MobiuOptimizer - wraps your PyTorch optimizer:

import torch
from mobiu_q import MobiuOptimizer

LICENSE_KEY = "your-license-key"

model = MyModel()
base_opt = torch.optim.Adam(model.parameters(), lr=0.0003)

opt = MobiuOptimizer(
    base_opt,                    # Your PyTorch optimizer
    license_key=LICENSE_KEY,
    method="adaptive",           # Best for RL/LLM
    use_soft_algebra=True,       # Enable Soft Algebra (default)
    sync_interval=50,            # Sync with cloud every N steps (default: 50)
    verbose=True
)

for epoch in range(100):
    loss = criterion(model(x), y)
    loss.backward()
    opt.step(loss.item())  # Pass loss value for Soft Algebra
    opt.zero_grad()

opt.end()

Quantum VQE (Simulation)

from mobiu_q import MobiuOptimizer
import numpy as np

LICENSE_KEY = "your-license-key"

params = np.random.randn(10)

opt = MobiuOptimizer(
    params,                      # Numpy array - auto-detects quantum mode
    license_key=LICENSE_KEY,
    method="standard",
    mode="simulation",           # Clean simulator
    use_soft_algebra=True
)

for step in range(100):
    params = opt.step(params, energy_fn)  # Auto-computes gradient

opt.end()

Quantum VQE (Real Hardware / FakeFez)

from mobiu_q import MobiuOptimizer

opt = MobiuOptimizer(
    params,
    license_key=LICENSE_KEY,
    method="standard",
    mode="hardware",             # Noisy hardware - uses SPSA
)

for step in range(100):
    params = opt.step(params, energy_fn)

opt.end()

QAOA (Combinatorial Optimization)

from mobiu_q import MobiuOptimizer

opt = MobiuOptimizer(
    params,
    license_key=LICENSE_KEY,
    method="deep",               # Best for rugged landscapes
    mode="hardware",
)

for step in range(150):
    params = opt.step(params, maxcut_cost_fn)

opt.end()

Manual Gradient (Quantum)

from mobiu_q import MobiuOptimizer, Demeasurement

opt = MobiuOptimizer(params, license_key=LICENSE_KEY, method="standard")

for step in range(100):
    energy = energy_fn(params)
    gradient = Demeasurement.finite_difference(energy_fn, params)
    params = opt.step(params, gradient, energy)

opt.end()

---

🔑 License Key

Get your key at app.mobiu.ai

# Option 1: Pass directly
opt = MobiuOptimizer(base_opt, license_key="your-key")

# Option 2: Environment variable
export MOBIU_Q_LICENSE_KEY="your-key"

# Option 3: Save to file (one time)
from mobiu_q import save_license_key
save_license_key("your-key")

---

🏆 Verified Benchmark Results

All benchmarks use fair A/B testing: Soft Algebra ON vs OFF, same seeds, same conditions.

🧪 Fair Testing Methodology

# PyTorch A/B test:
opt_baseline = MobiuOptimizer(base_opt, license_key=KEY, use_soft_algebra=False)
opt_mobiu = MobiuOptimizer(base_opt, license_key=KEY, use_soft_algebra=True)

# Quantum A/B test:
opt_baseline = MobiuOptimizer(params, license_key=KEY, use_soft_algebra=False)
opt_mobiu = MobiuOptimizer(params, license_key=KEY, use_soft_algebra=True)

# Same seed, same problem, same everything - only SA differs

🎮 Reinforcement Learning

Environment	Improvement	Win Rate	p-value	Cohen's d
LunarLander-v3	+146.9%	93.3%	< 0.000001	+1.50
Atari Breakout	+54.2%	100%	-	-

LunarLander: 30 seeds, 1000 episodes each. Atari: 3 seeds, 200 episodes each.

💰 Portfolio Optimization

Noise Level	Improvement	Win Rate	p-value	Cohen's d
1%	+16.8%	100%	< 0.000001	+0.94
10%	+13.7%	100%	< 0.000001	+0.99
50%	+12.8%	100%	< 0.000001	+0.98

100 seeds per noise level. Sharpe ratio optimization on AAPL, GOOGL, MSFT, AMZN, TSLA.

Overall: 300/300 wins (100%), average improvement +14.5%

⚛️ Quantum VQE on IBM FakeFez

Molecule	Qubits	Improvement	Win Rate
H₂	2	+52.5%	100%
BeH₂	6	+55.1%	100%
LiH	4	+34.5%	100%

🎯 QAOA on IBM FakeFez

Problem	Improvement	p-value
MaxCut	+45.1%	0.0003

💳 Finance (Other)

Problem	Improvement
Credit Risk	+52.3%

---

🛠️ Troubleshooting

Not Improving?

1. Switch optimizer: Try NAdam or Momentum (Quantum mode)
2. Switch method: standard ↔ adaptive ↔ deep
3. Adjust LR: Diverging → lower by 2-5x, stuck → raise by 2x
4. Reduce sync_interval: Try sync_interval=1 for more frequent updates (PyTorch)

Quantum Specific

• Noisy results? Use mode="hardware" (enables SPSA)
• Clean simulator? Use mode="simulation" (uses finite difference)

PyTorch Specific

• High latency? Increase sync_interval (default: 50)
• Not learning? Decrease sync_interval to 1

---

📖 API Reference

MobiuOptimizer (Universal)

MobiuOptimizer(
    optimizer_or_params,          # torch.optim.Optimizer OR np.ndarray
    license_key: str,
    method: str = "adaptive",     # "standard", "deep", "adaptive"
    mode: str = "simulation",     # "simulation", "hardware"
    use_soft_algebra: bool = True,
    sync_interval: int = 50,      # Cloud sync frequency (PyTorch only)
    verbose: bool = True
)

Auto-detection:

• If optimizer_or_params has .step(), .param_groups, .zero_grad() → PyTorch mode
• Otherwise → Quantum mode (delegates to MobiuQCore)

MobiuQCore (Quantum - Low-level)

For advanced quantum use cases:

from mobiu_q import MobiuQCore

MobiuQCore(
    license_key: str,
    method: str = "standard",
    mode: str = "simulation",
    base_optimizer: str = "Adam", # Optimizer name (string!)
    base_lr: float = None,        # Auto-computed if None
    use_soft_algebra: bool = True,
    verbose: bool = True
)

---

🔬 How It Works

Mobiu-Q is based on Soft Algebra from Klein/Maimon theory:

SoftNumber multiplication (ε²=0):
(a, b) × (c, d) = (ad + bc, bd)

The Super-Equation Δ† detects emergence moments for adaptive scaling.

---

💰 Pricing

Tier	Price	Runs
Free	$0	20 runs/month
Pro	$19/month	Unlimited

Get your key at app.mobiu.ai

---

🧑‍🔬 Scientific Foundation

Based on Soft Numbers theory developed by Dr. Moshe Klein and Prof. Oded Maimon (Tel Aviv University), as presented in their book on Soft Logic and Soft Numbers.

---

📚 Links

• Website: mobiu.ai
• App: app.mobiu.ai
• PyPI: pypi.org/project/mobiu-q

---

© 2025 Mobiu Technologies. All rights reserved.