mobiu-q 2.7.8

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q v2.7.8

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

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⚡ Quick Start

from mobiu_q import MobiuOptimizer

# PyTorch (RL, LLM, Deep Learning)
opt = MobiuOptimizer(torch_optimizer, method="adaptive")

# Quantum VQE (clean simulator)
opt = MobiuOptimizer(params, method="standard", mode="simulation")

# Quantum VQE (real/noisy hardware)
opt = MobiuOptimizer(params, method="standard", mode="hardware")

# QAOA (combinatorial optimization)
opt = MobiuOptimizer(params, method="deep", mode="hardware")

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🔧 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

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(params, use_soft_algebra=True)   # Default - SA enabled
opt = MobiuOptimizer(params, use_soft_algebra=False)  # Baseline - SA disabled

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📦 Installation

pip install mobiu-q

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🎯 Usage Examples

PyTorch (RL / LLM / Deep Learning)

import torch
from mobiu_q import MobiuOptimizer

model = MyModel()
base_opt = torch.optim.Adam(model.parameters(), lr=0.0003)
opt = MobiuOptimizer(base_opt, method="adaptive")

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

opt.end()

Quantum VQE (Simulation)

from mobiu_q import MobiuOptimizer
import numpy as np

params = np.random.randn(10)
opt = MobiuOptimizer(params, method="standard", mode="simulation")

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, method="standard", mode="hardware")

for step in range(100):
    params = opt.step(params, energy_fn)  # Uses SPSA gradient

opt.end()

QAOA (Combinatorial Optimization)

from mobiu_q import MobiuOptimizer

opt = MobiuOptimizer(params, method="deep", mode="hardware")

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

opt.end()

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🏆 Verified Benchmark Results

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

🧪 Fair Testing Methodology

# How we test - you can reproduce this yourself:
opt_baseline = MobiuOptimizer(params, use_soft_algebra=False)  # SA OFF
opt_mobiu = MobiuOptimizer(params, use_soft_algebra=True)      # SA ON

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

This ensures improvements come from Soft Algebra, not different hyperparameters.

⚛️ 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

🎮 Reinforcement Learning

Environment	Improvement	Win Rate
LunarLander-v3	+127.8%	96.7%
MuJoCo InvertedPendulum	+111%	100%
MuJoCo Hopper	+41%	80%

💰 Finance

Problem	Improvement
Credit Risk	+52.3%
Portfolio Optimization	+51.7%

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🛠️ Troubleshooting

Not Improving?

1. Switch optimizer: Try NAdam or Momentum
2. Switch method: standard ↔ adaptive ↔ deep
3. Adjust LR: Diverging → lower by 2-5x, stuck → raise by 2x

Quantum Specific

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

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🔬 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.

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💰 Pricing

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

Get your key at app.mobiu.ai

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🧑‍🔬 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.

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📚 Links

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

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