q-anchor-federated-quantum-learning

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:

1. Client drift: Non-IID data causes local models to diverge from global optimum (classical FL problem)
2. 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

Related Skills

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