mobiu-q 1.4.0

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q

Soft Algebra Optimizer for Quantum Computing

Mobiu-Q achieves +62% on VQE and +20% on QAOA compared to Adam optimizer, using a novel Soft Algebra approach that's resilient to quantum noise.

Installation

pip install mobiu-q

Quick Start

VQE (Molecular Simulation)

from mobiu_q import MobiuQCore, Demeasurement

# Initialize optimizer for VQE
opt = MobiuQCore(
    license_key="your-license-key",
    mode="standard",      # or "noisy" for hardware
    problem="vqe"         # default
)

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

opt.end()

QAOA (Combinatorial Optimization)

from mobiu_q import MobiuQCore, Demeasurement

# Initialize optimizer for QAOA
opt = MobiuQCore(
    license_key="your-license-key",
    mode="noisy",         # QAOA typically uses SPSA
    problem="qaoa"        # Use Super-Equation Δ†
)

# Optimization loop
for step in range(150):
    energy = qaoa_expectation(params)
    gradient = spsa_gradient(energy_fn, params)
    params = opt.step(params, gradient, energy)

opt.end()

Benchmarks

VQE (Quantum Chemistry)

Molecule	Improvement vs Adam	p-value
H₂	+62%	< 10⁻⁵⁷
LiH	+50.6%	< 10⁻¹²
HeH⁺	+68%	< 10⁻⁴⁰

QAOA (Combinatorial, noise=10%)

Problem	Depth	Improvement	p-value
MaxCut	p=5	+38.49%	< 0.001
Vertex Cover	p=5	+35.77%	0.011
Max Independent Set	p=5	+30.62%	< 0.001

Hardware Validation

Tested on IBM Quantum Eagle (127-qubit):

• Adam: Crashed to -1.681 Ha (non-physical)
• Mobiu-Q: Converged to -1.176 Ha (99.6% accuracy)

Parameters

Parameter	Values	Description
mode	"standard", "noisy"	Gradient type
problem	"vqe", "qaoa"	Problem type
base_lr	float	Base learning rate (auto-set by mode)

How It Works

VQE: Trust Ratio

For smooth energy landscapes (molecular chemistry), Mobiu-Q uses the Trust Ratio:

φ = |S.real| / (|S.real| + |S.soft| + ε)

High trust = stable gradient = larger learning rate.

QAOA: Super-Equation Δ†

For rugged combinatorial landscapes, Mobiu-Q uses the Super-Equation from Universal Attention Field Theory:

Δ† = κ · Du[sin(πS)] · g(τ,α) · Γ(a,β) · √(b·g(τ,α))

This identifies optimal "emergence points" where the optimization should act aggressively.

Pricing

• Free: 20 runs/month
• Pro: $19/month unlimited

Get your license at app.mobiu.ai

License

Proprietary. See LICENSE for details.

Citation

@software{mobiu_q,
  author = {Angel, Ido},
  title = {Mobiu-Q: Soft Algebra Optimizer for Quantum Computing},
  year = {2025},
  url = {https://github.com/mobiuai/mobiu-q}
}

References

• Klein, M. & Maimon, O. "Foundations of Soft Logic" (2023)
• Angel, I. "Universal Attention Field Theory" (2025)

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