mobiu-q 2.5.6

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q v2.5.6

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

---

🚀 What's New in v2.5.6

• Comprehensive Validation: 30+ problems tested across 7 domains
• Quantum Hardware: Validated on IBM FakeFez realistic noise models
• Multi-Optimizer: Adam, NAdam, AMSGrad, SGD, Momentum, LAMB

---

🏆 Verified Benchmark Results

All benchmarks compare Optimizer + Soft Algebra vs Optimizer alone. Same learning rate, same seeds, fair A/B test.

🎮 Reinforcement Learning

Environment	Improvement	p-value	Win Rate
LunarLander-v3	+129.7%	<0.001	96.7%
MuJoCo InvertedPendulum	+118.6%	0.001	100%
MuJoCo Hopper	+41.2%	0.007	80%

📐 Classical Optimization

Function	Improvement	Description
Rosenbrock	+75.8%	Valley navigation
Beale	+62.0%	Plateau escape
Sphere	+31.1%	Convex baseline

⚛️ Quantum VQE - Condensed Matter

Model	Improvement
SSH Model (Topological)	+61.0%
XY Model	+60.8%
Ferro Ising	+45.1%
Transverse Ising	+42.0%
Heisenberg XXZ	+20.8%
Kitaev Chain	+20.4%
Hubbard Dimer	+14.1%

⚛️ Quantum VQE - Chemistry

Molecule	Improvement
FakeFez H₂	+52.4% (p=0.043)
He Atom	+51.2%
H₂ Molecule	+46.6%
H₃⁺ Chain	+42.0%
LiH Molecule	+41.4%
BeH₂ Molecule	+37.8%

🎯 QAOA (Combinatorial Optimization)

Problem	Improvement	Wins
FakeFez MaxCut	+45.1%	p=0.0003
Vertex Cover	+31.9%	51/60
Max Independent Set	+31.9%	51/60
MaxCut	+21.5%	45/60

💰 Finance (QUBO)

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

💊 Drug Discovery

Task	Improvement	Config
Binding Affinity	+12.2%	AMSGrad + standard

---

📦 Installation

pip install mobiu-q

---

⚡ Quick Start

1. Reinforcement Learning

from mobiu_q import MobiuQCore

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="adaptive",
    base_optimizer="Adam",
    base_lr=0.0003
)

for episode in range(1000):
    episode_return = run_episode(policy)
    gradient = compute_policy_gradient()
    policy_params = opt.step(policy_params, gradient, episode_return)

opt.end()

2. VQE (Quantum Chemistry)

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="standard",
    mode="hardware",
    base_optimizer="Adam"
)

for step in range(100):
    energy = compute_vqe_energy(params)
    grad = finite_difference_gradient(energy_fn, params)
    params = opt.step(params, grad, energy)

opt.end()

3. QAOA (Combinatorial Optimization)

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="deep",
    mode="hardware",
    base_optimizer="SGD",
    base_lr=0.1
)

for step in range(150):
    cost = compute_qaoa_cost(params)
    grad = spsa_gradient(cost_fn, params)
    params = opt.step(params, grad, cost)

opt.end()

4. Finance (Portfolio/Credit Risk)

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="standard",
    base_optimizer="Adam",
    base_lr=0.01
)

for epoch in range(100):
    loss = compute_portfolio_loss(weights)
    gradient = compute_gradients()
    weights = opt.step(weights, gradient, loss)

opt.end()

---

🔧 Configuration

📖 See CONFIGURATION_GUIDE.md for complete details

Methods

Method	Best For	LR
standard	VQE, Chemistry, Finance	0.01
deep	QAOA, Noisy Hardware	0.1
adaptive	RL, High-variance	0.0003

Base Optimizers

Optimizer	Best For
Adam	Default, most cases
AdamW	LLM, weight decay
SGD	QAOA
AMSGrad	Drug Discovery
NAdam	Alternative to Adam
Momentum	RL alternative
LAMB	Large batch

Important: Optimizer names are case-sensitive!

---

🛠️ Troubleshooting

If optimization is not improving or diverging, try these adjustments:

1. Switch Base Optimizer

Different optimizers work better for different problems:

# If Adam isn't working, try:
opt = MobiuQCore(license_key="KEY", base_optimizer="NAdam")

# Or try Momentum:
opt = MobiuQCore(license_key="KEY", base_optimizer="Momentum")

2. Switch Method

If This Fails	Try This
standard	adaptive
adaptive	deep
deep	standard

# If standard isn't working:
opt = MobiuQCore(license_key="KEY", method="adaptive")

3. Switch Mode

For quantum problems, if simulation mode isn't working:

# Try hardware mode (more aggressive noise filtering):
opt = MobiuQCore(license_key="KEY", mode="hardware")

4. Adjust Learning Rate

Scenario	Recommendation
Diverging	Lower LR by 2-5x
No improvement	Increase LR by 2x
QAOA	Use LR=0.1
RL	Use LR=0.0003

---

🔬 How It Works

Mobiu-Q is based on Soft Algebra (ε²=0):

(a, b) × (c, d) = (ad + bc, bd)

Evolution Law:

S_{t+1} = (γ · S_t) · Δ_t + Δ_t

---

💰 Pricing

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

Get your key at app.mobiu.ai

---

📊 Summary by Domain

Domain	Best Result	Avg Improvement
RL	+129.7%	~96%
Classical Opt	+75.8%	~56%
Condensed Matter	+61.0%	~38%
Quantum Chemistry	+52.4%	~45%
Finance	+52.3%	~52%
QAOA	+45.1%	~32%
Drug Discovery	+12.2%	+12%

---

🧑‍🔬 Scientific Foundation

• Dr. Moshe Klein – Soft Logic and Soft Numbers
• Prof. Oded Maimon – Tel Aviv University

---

📚 Links

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

---

© 2025 Mobiu Technologies. All rights reserved.