mobiu-q 1.0.4

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q

Mobiu-Q is a next-generation optimizer built on Soft Algebra and Demeasurement theory, enabling stable and efficient optimization in quantum variational algorithms (VQE, QAOA).

✨ Features

• Soft Algebra update rule for stable convergence
• SPSA Demeasurement for noisy hardware
• Adaptive "Noisy Mode" presets
• Validated on real quantum hardware (IBM)

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📦 Installation

pip install mobiu-q

🔑 License

from mobiu_q import activate_license

activate_license("YOUR-LICENSE-KEY")

• Free tier: 5 runs/month
• Pro tier: Unlimited runs

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🚀 Quick Start (Simulation)

Best for clean simulations or statevector backends.

import numpy as np
from mobiu_q import MobiuQCore, Demeasurement, get_energy_function

energy_fn = get_energy_function("h2_molecule")

# Initialize in standard mode
opt = MobiuQCore(mode="standard") 

params = np.random.uniform(-np.pi, np.pi, 6)

for step in range(50):
    E = energy_fn(params)
    grad = Demeasurement.finite_difference(energy_fn, params)
    params = opt.step(params, grad, E)

opt.end()  # End session

⚡ Real Hardware / Shot Noise

When running on noisy quantum computers (IBM, IonQ) or simulators with shot noise:

# Initialize in noisy mode (robust learning)
opt = MobiuQCore(mode="noisy") 

for step in range(100):
    # SPSA returns gradient AND energy estimate (saves 50% measurements)
    grad, E = Demeasurement.spsa(energy_fn, params, c_shift=0.1)
    params = opt.step(params, grad, E)

opt.end()

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📊 Performance Results

Clean Simulation

Tested on H2 molecule (6 params), 100 seeds:

Optimizer	Gap to Ground State	Improvement
Adam	0.089	-
Mobiu-Q	0.034	+62% ✅

Shot Noise Simulation

Tested on Transverse Ising (4 qubits), 30 seeds:

Shots	Adam Gap	Mobiu-Q Gap	Improvement	p-value
1000	1.63	1.48	+9.2%	0.002 ✅
500	1.65	1.49	+9.8%	0.002 ✅
50	2.00	1.82	+9.2%	0.009 ✅

Real Quantum Hardware (IBM Fez)

H2 molecule optimization:

Metric	Result
Initial gap	0.22
Final gap	0.034
Improvement	85% ✅

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💡 Choosing the Right Mode

Scenario	Mode	Gradient Method
Clean simulation (statevector)	standard	finite_difference
Shot noise simulation	noisy	spsa
Real quantum hardware	noisy	spsa

Mode Settings

Mode	Learning Rate	Best For
standard	0.05	Simulators (Qiskit Aer, PennyLane, Cirq)
noisy	0.02	Real hardware (IBM, IonQ, Rigetti)

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📚 Built-in Problems

from mobiu_q import list_problems, get_energy_function, get_ground_state_energy

print(list_problems())
# ['h2_molecule', 'lih_molecule', 'transverse_ising', 'heisenberg_xxz', ...]

energy_fn = get_energy_function("h2_molecule")
E0 = get_ground_state_energy("h2_molecule")

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⚙️ API Reference

MobiuQCore

MobiuQCore(
    license_key=None,       # Your license key (or use activate_license())
    mode="standard",        # 'standard' or 'noisy'
    base_lr=None,           # Custom learning rate (overrides mode)
    verbose=True            # Print session messages
)

Methods:

• step(params, gradient, energy) → updated params
• end() → close session

Demeasurement

# For clean simulations (2*N function calls)
grad = Demeasurement.finite_difference(fn, params)

# For noisy environments (only 2 function calls!)
grad, energy = Demeasurement.spsa(fn, params, c_shift=0.1)

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🔥 Full Example: IBM Hardware

from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2
from mobiu_q import MobiuQCore, Demeasurement

service = QiskitRuntimeService(channel="ibm_quantum")
backend = service.least_busy(simulator=False, min_num_qubits=5)
estimator = EstimatorV2(mode=backend)

opt = MobiuQCore(mode="noisy")

for step in range(60):
    grad, energy = Demeasurement.spsa(
        lambda p: estimator.run([(circuit, observable)]).result()[0].data.evs.item(),
        params,
        c_shift=0.12
    )
    params = opt.step(params, grad, energy)

opt.end()

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