q-anchor-federated-quantum-learning - SKILL.md Agent Skill

name: q-anchor-federated-quantum-learning description: "Q-ANCHOR architecture for Quantum Federated Learning (QFL) that addresses double-drift phenomenon (client drift from non-IID data + hardware bias from noisy quantum gradients). Uses ZNE-guided server anchoring and stateful client correction. Proves convergence under noisy quantum gradient estimates. Activation: Q-ANCHOR, federated quantum learning, QFL, zero-noise extrapolation, quantum federated aggregation, quantum hardware bias, client drift, non-IID quantum data" metadata: arxiv_id: "2605.30075" published: "2026-05-28" authors: "Hoang M. Ngo, Quan Nguyen, Wanli Xing, My T. Thai" tags: [quantum, federated-learning, distributed-systems, error-mitigation, qml]

Core Problem: Double-Drift in Quantum Federated Learning

QFL faces two simultaneous convergence barriers:

Client drift: Non-IID data causes local models to diverge from global optimum (classical FL problem)
Hardware bias: Noisy quantum gradient estimates create persistent error floor that standard FedAvg cannot correct (quantum-specific problem)

Standard FedAvg aggregation fails because it averages both signal and hardware bias, creating a persistent error floor.

Q-ANCHOR Architecture

Server-Side: ZNE-Guided Anchoring

Global update = ZNE_corrected(average(local_gradients))

Server collects quantum circuit outputs from clients
Applies zero-noise extrapolation (ZNE) using noise scaling factors
Extrapolates to zero-noise limit before aggregation
Anchors global update to hardware-corrected estimate

Client-Side: Stateful Correction

Corrected client gradient = local_gradient - hardware_bias_estimate

Each client maintains running estimate of hardware bias
Bias estimated via shadow circuits / calibration routines
Stateful tracking prevents bias accumulation across rounds

Convergence Theory

Q-ANCHOR convergence proof shows:

Mitigates classical client drift (standard FL convergence rate)
Actively reduces hardware-bias floor (quantum-specific improvement)
Achieves significantly more stable training than conventional FL baselines

Implementation Pattern

# Pseudocode for Q-ANCHOR server update
def q_anchor_server_update(client_gradients, noise_scales=[1, 2, 3]):
    # Collect gradient measurements at multiple noise levels
    noisy_averages = []
    for scale in noise_scales:
        scaled_gradients = [scale_noise(g, scale) for g in client_gradients]
        noisy_averages.append(average(scaled_gradients))
    
    # ZNE extrapolation to zero noise
    zne_corrected = richardson_extrapolation(noisy_averages, noise_scales)
    
    return zne_corrected

Key Metrics

Hardware bias floor: Persistent error from quantum noise, measured via shadow circuits
Client drift: Divergence between local and global optima, measured via gradient norm difference
ZNE effectiveness: Ratio of corrected vs uncorrected gradient variance

Pitfalls

ZNE overhead: Requires multiple noise scale evaluations per round → 3-5x circuit execution cost
Shadow circuit design: Must match parameterized ansatz to be useful for bias estimation
Non-IID + noise coupling: Both effects interact non-linearly; cannot treat independently

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