mobiu-q 2.5.1

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q (v2.5.1)

Universal Physics-Aware Optimizer for Stochastic Systems

Mobiu-Q is the first optimizer based on Soft Algebra, developed by Dr. Moshe Klein and Prof. Oded Maimon. By mathematically decomposing gradients into Potential ($a_t$) and Realization ($b_t$), it filters out noise in real-time.

Works across Quantum Computing, Reinforcement Learning, LLM Fine-Tuning, and FinTech.

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🚀 What's New in v2.5.0

• New Method Names: standard, deep, adaptive (legacy vqe/qaoa/rl still work!)
• Noise Robustness: +32.5% more robust to quantum hardware noise
• 80% Win Rate: Outperforms standard optimizers across all noise levels
• LLM Support: +18% improvement on soft prompt tuning

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🏆 Benchmark Results

Noise Robustness (IBM FakeBackend)

Condition	Momentum	Mobiu-Q	Winner
IDEAL	-2.19	-1.29	Momentum
NOISY	+0.20	-0.30	Mobiu-Q ✅

Key Finding:

• Momentum degradation under noise: +109% (breaks down)
• Mobiu-Q degradation under noise: +77% (stays stable)
• Mobiu-Q is 32.5% MORE ROBUST to noise!

Comprehensive Noise Test

Qubits	Noise Level	SA Gain	Win Rate
2	all levels	+27-65%	5/5 ✅
4	all levels	+5-19%	4/5 ✅
6	all levels	+2-14%	3/5 ✅

Overall: 80% win rate (12/15 tests) with +5% to +65% improvement

LLM Soft Prompt Tuning

Config	Improvement	Win Rate
Momentum+SA	+18.1%	3/3 ✅

Quantum Chemistry (VQE)

Molecule	Improvement
H2	+46.6%
LiH	+41.4%
BeH2	+37.8%
He Atom	+51.2%

Reinforcement Learning

Environment	Improvement	Win Rate
LunarLander	+129.7%	96.7%
MuJoCo	+118.6%	100%

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📦 Installation

pip install mobiu-q

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⚡ Quick Start

1. Standard (Quantum VQE, Chemistry)

from mobiu_q import MobiuQCore, Demeasurement

opt = MobiuQCore(license_key="YOUR-KEY", method="standard")

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

opt.end()

2. Deep (Complex Circuits, Noisy Hardware)

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="deep",
    mode="hardware"  # For quantum hardware / noisy simulation
)

for step in range(150):
    grad, energy = Demeasurement.spsa(energy_fn, params)
    params = opt.step(params, grad, energy)

opt.end()

3. Adaptive (RL, LLM Fine-Tuning)

opt = MobiuQCore(license_key="YOUR-KEY", method="adaptive")

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()

4. LLM Soft Prompt Tuning

opt = MobiuQCore(license_key="YOUR-KEY", method="adaptive")

for step in range(50):
    loss = compute_loss(soft_tokens, model, batch)
    grad = compute_gradient(loss, soft_tokens)
    soft_tokens = opt.step(soft_tokens, grad, loss)

opt.end()

5. Multi-Seed Experiments (1 billing session)

opt = MobiuQCore(license_key="YOUR-KEY")

for seed in range(10):
    opt.new_run()  # Resets state, keeps session open
    params = init_params(seed)
    # ... optimization loop ...

opt.end()  # All 10 seeds count as 1 run

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🎛️ Configuration

Methods

Method	Legacy	Use Case	Default LR
standard	vqe	Smooth landscapes, chemistry, physics	0.01-0.02
deep	qaoa	Deep circuits, noisy hardware	0.1
adaptive	rl	RL, LLM fine-tuning, high-variance	0.0003

Modes

Mode	Use Case
simulation	Clean simulations
hardware	Quantum hardware, noisy sims

Optimizers

⚠️ Optimizer names are case-sensitive!

# Use default (Adam)
opt = MobiuQCore(method="standard")

# Alternative optimizer
opt = MobiuQCore(method="deep", base_optimizer="NAdam")

Available optimizers:

• Adam (default) - Best overall
• NAdam - Strong on deep circuits
• Momentum - Best for noisy hardware (+18.1% on LLM)
• AMSGrad - Alternative for standard
• SGD - Simple baseline
• LAMB - Large batch training

Disable Soft Algebra

For A/B testing:

opt = MobiuQCore(method="standard", use_soft_algebra=False)

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🧠 How It Works

The Core Innovation: "Noise Hallucination" Prevention

Standard optimizers assume lower objective values always indicate better solutions. In noisy environments, this fails. Mobiu-Q uses Soft Algebra to distinguish real progress from noise.

SoftNumber Multiplication (Nilpotent ε²=0)

(a, b) * (c, d) = (ad + bc, bd)

State Evolution

S_{t+1} = (γ · S_t) · Δ_t + Δ_t

Where:

• a_t (Potential): Curvature signal
• b_t (Realized): Actual improvement
• Δ† (Super-Equation): Emergence detection for deep/adaptive

Method-Specific Logic

Method	Primary Mechanism	Best For
standard	Trust Ratio + Gradient Warping	Smooth energy landscapes
deep	Super-Equation Δ†	Rugged, multimodal, noisy
adaptive	Trust + Emergence + Warping	High-variance, sparse reward

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📊 When to Use Mobiu-Q

✅ Use Mobiu-Q when:

• High noise/variance (quantum hardware, RL, stochastic finance)
• Deep circuits with many parameters
• Noisy quantum hardware (IBM, IonQ, etc.)
• LLM fine-tuning with limited data
• Standard optimizers diverge or get stuck

❌ Skip Mobiu-Q when:

• Clean, convex problems
• Deterministic, low-noise environments

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🔑 Pricing

Tier	Runs/Month	Features
Free	20	Testing & students
Pro	Unlimited	Priority, all features

Get your License Key

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📚 API Reference

MobiuQCore

MobiuQCore(
    license_key: str,
    method: str = "standard",      # "standard", "deep", "adaptive"
    mode: str = "simulation",      # "simulation" or "hardware"
    base_lr: float = None,         # Auto if None
    base_optimizer: str = "Adam",  # Case-sensitive!
    use_soft_algebra: bool = True,
    offline_fallback: bool = True
)

Methods:

• step(params, gradient, energy) → Updated params
• new_run() → Reset for new seed (same session)
• end() → End session (counts usage)
• check_usage() → Get remaining runs

Demeasurement

# For standard (smooth)
grad = Demeasurement.finite_difference(energy_fn, params)
grad = Demeasurement.parameter_shift(circuit_fn, params)

# For deep/hardware (noisy)
grad, energy = Demeasurement.spsa(energy_fn, params)

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🔬 Scientific Foundation

Mobiu-Q is based on Soft Algebra, developed by:

• Dr. Moshe Klein - Mathematician, Soft Logic and Soft Numbers
• Prof. Oded Maimon - Tel Aviv University, Industrial Engineering

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📖 Citation

@software{mobiu_q,
  title = {Mobiu-Q: Soft Algebra Optimizer for Stochastic Systems},
  author = {Angel, Ido and Klein, Moshe and Maimon, Oded},
  year = {2024},
  url = {https://mobiu.ai}
}

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