qaoa-zne-portfolio

name: qaoa-zne-portfolio description: "QAOA + Zero Noise Extrapolation (ZNE) workflow for multi-objective portfolio optimization on real IBM Quantum hardware. Demonstrates QAOA with error mitigation outperforming classical greedy baselines on 88-variable problems with carbon sequestration, biodiversity, and social impact objectives. Use when: (1) running QAOA on real quantum hardware, (2) applying ZNE for error mitigation, (3) multi-objective portfolio optimization, (4) ESG/green finance quantum applications, (5) NISQ-era quantum advantage demonstration." license: Complete terms in LICENSE.txt metadata: arxiv_id: "2602.09047" published: "2026-02-13" authors: "Hugo José Ribeiro" tags: [QAOA, ZNE, portfolio-optimization, IBM-Quantum, error-mitigation, ESG, multi-objective]

QAOA + ZNE for Multi-Objective Portfolio Optimization

Core Concept

Applies the Quantum Approximate Optimization Algorithm (QAOA) combined with Zero Noise Extrapolation (ZNE) error mitigation to solve multi-objective portfolio optimization problems on real IBM Quantum hardware. Demonstrates that QAOA+ZNE consistently outperforms classical greedy baselines on 88-variable problems.

QAOA+ZNE Workflow

Step 1: Problem Formulation

Encode portfolio optimization as QUBO:

• Variables: Binary selection of assets/projects (88 variables in the study)
• Objectives: Carbon sequestration, biodiversity connectivity, social impact metrics
• Constraints: Cardinality constraints (fixed number of selections), budget limits
• Objective function: Weighted sum of objectives converted to Ising Hamiltonian

Step 2: QAOA Circuit Construction

|0⟩^n → H^{⊗n} → [U_C(γ) · U_M(β)]^p → Measure

• Cost unitary U_C(γ): e^{-iγH_C} encodes the portfolio objective
• Mixer unitary U_M(β): e^{-iβH_M} explores solution space (typically X-mixer)
• Depth p: Number of QAOA layers (higher p → better approximation, deeper circuit)

Step 3: Zero Noise Extrapolation (ZNE)

Error mitigation to counteract NISQ hardware noise:

1. Noise scaling: Intentionally amplify noise by stretching gate durations or inserting identity gates
2. Measure at multiple noise levels: Run circuit at noise factors λ = {1, 2, 3, ...}
3. Extrapolate to zero noise: Fit polynomial (Richardson or exponential) to noisy results and extrapolate to λ=0

ZNE variants:

• Gate folding: Replace gate G → G·G†·G to triple effective noise
• Unitary folding: Replace G → G·G†·G^n for arbitrary noise scaling
• Richardson extrapolation: Linear polynomial fit, most common

Step 4: Classical Optimization Loop

for iteration in range(max_iters):
    # Quantum: run QAOA+ZNE circuit
    expectation = run_qaoa_zne(parameters, backend=ibm_hardware)
    
    # Classical: optimize parameters
    parameters = optimizer.step(expectation, parameters)
    
    # Check convergence
    if converged(expectation):
        break

Key Results

• QAOA+ZNE on IBM Quantum hardware outperforms classical greedy baseline
• 88-variable problem with 3 objectives (carbon, biodiversity, social impact)
• Error mitigation (ZNE) is essential — raw QAOA results degraded by hardware noise
• Demonstrates practical quantum advantage for ESG portfolio optimization

Implementation Tips

• Use Qiskit Runtime for efficient ZNE execution on IBM hardware
• Start with low QAOA depth (p=1,2) on real hardware due to coherence limits
• ZNE shot budget: multiply shots by number of noise levels (typically 3-5×)
• Constrained optimization: use constraint-native encoding or penalty terms
• Compare against classical baselines: greedy, simulated annealing, Gurobi

Applications

• Carbon credit portfolio optimization
• ESG investment allocation
• Multi-objective territorial planning
• Any QUBO problem benefiting from error-mitigated quantum optimization

Activation Keywords

• QAOA ZNE
• zero noise extrapolation
• error mitigation QAOA
• quantum portfolio optimization
• IBM Quantum hardware
• multi-objective QUBO
• ESG quantum
• carbon credit portfolio
• QAOA error mitigation
• NISQ optimization
• Richardson extrapolation
• gate folding