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arxiv: 2605.30075 · v1 · pith:4OEUYHORnew · submitted 2026-05-28 · 💻 cs.LG · cs.DC

Q-ANCHOR: Federated Quantum Learning with ZNE-guided Correction

Hoang M. Ngo , Quan Nguyen , Wanli Xing , My T. Thai This is my paper

Pith reviewed 2026-06-29 09:02 UTC · model grok-4.3

classification 💻 cs.LG cs.DC
keywords quantum federated learningzero-noise extrapolationclient drifthardware biasFedAvg convergencenon-IID dataquantum noise mitigation
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The pith

Q-ANCHOR uses zero-noise extrapolation at the server and stateful client corrections to reduce the hardware bias floor in quantum federated learning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard federated averaging in quantum settings produces a persistent error floor because noisy quantum gradients create hardware bias that averaging cannot remove, on top of client drift from non-identical data. The paper proves that this double drift prevents convergence to the true optimum under realistic hardware conditions. Q-ANCHOR counters both problems by anchoring server updates with zero-noise extrapolation while clients apply stateful corrections. Convergence analysis shows the method lowers the bias floor and stabilizes training. Experiments confirm more reliable performance than plain FedAvg on non-IID quantum data.

Core claim

The central claim is that Q-ANCHOR, by applying zero-noise extrapolation to anchor server aggregation and stateful correction on clients, mitigates classical client drift while actively reducing the hardware-bias floor that standard averaging leaves uncorrected, as established by the convergence theory under non-IID data and noisy quantum gradients.

What carries the argument

Q-ANCHOR architecture that anchors server updates with zero-noise extrapolation while applying stateful client correction to suppress both client drift and hardware-induced bias.

If this is right

  • The global model converges without a persistent hardware error floor under non-IID conditions.
  • Training stability improves over standard FedAvg in the presence of quantum gradient noise.
  • Both classical drift and hardware bias are addressed simultaneously by the same aggregation rule.
  • The architecture remains compatible with low-communication federated protocols.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same anchoring idea could be tested in classical federated learning with simulated gradient noise to isolate the extrapolation benefit.
  • Real-device validation would require measuring bias reduction separately from statistical variance across multiple hardware runs.
  • If ZNE overhead scales with circuit depth, the method may favor shallower quantum models over deeper ones.

Load-bearing premise

Zero-noise extrapolation applied at the server can measurably reduce hardware bias even when client data distributions are non-identical.

What would settle it

A run of Q-ANCHOR on real quantum hardware with non-IID client data that leaves the hardware-bias floor unchanged or higher than baseline FedAvg would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.30075 by Hoang M. Ngo, My T. Thai, Quan Nguyen, Wanli Xing.

Figure 1
Figure 1. Figure 1: Impact of hardware noise on gradient bias. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Performance comparison of Q-ANCHOR and other FL baselines under depolarizing noise p = 0.01. demonstrate more stable performance compared with FedAvg and SCAFFOLD. One limitation of this work is that our empirical evaluation is conducted in simulated noisy quantum environments. Future work will examine Q-ANCHOR in real quantum hardware. References [1] Vojtech Havlí ˇ cek, Antonio D. Córcoles, Kristan Temme… view at source ↗
Figure 3
Figure 3. Figure 3: Visualization of the eight base images used to generate the Binary Blobs dataset, compared [PITH_FULL_IMAGE:figures/full_fig_p032_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Non-IID client distribution (Dirichlet α = 0.3) 32 [PITH_FULL_IMAGE:figures/full_fig_p032_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Performance comparison of Q-ANCHOR and other FL algorithms under depolarizing noise p = 0.02 with analytic gradients [PITH_FULL_IMAGE:figures/full_fig_p033_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Performance comparison of Q-ANCHOR and other FL algorithms under depolarizing noise p = 0.03 with analytic gradients. F Performance of Q-ANCHOR under varying finite-shot variance σ 2 q The precision of gradient estimation in Variational Quantum Algorithms (VQAs) is inherently tied to the number of measurement shots used to evaluate quantum observables. As shown in [PITH_FULL_IMAGE:figures/full_fig_p033_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Impact of finite measurement shots on statistical variance and runtime. [PITH_FULL_IMAGE:figures/full_fig_p034_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Impact of number of shots on Q-ANCHOR training dynamics under depolarizing noise p = 0.01 [PITH_FULL_IMAGE:figures/full_fig_p034_8.png] view at source ↗
read the original abstract

Quantum Federated Learning (QFL) offers a promising framework to train quantum models across distributed clients while keeping data strictly local. Due to its simplicity and low communication overhead, Federated Averaging (FedAvg) is the standard aggregation choice in QFL literature. However, deploying QFL on practical hardware exposes a severe double-drift phenomenon: the global model is simultaneously derailed by client drift from non-IID data and hardware bias from noisy quantum gradient estimates. In this work, we first analyze the convergence of FedAvg under these realistic conditions, mathematically demonstrating that quantum hardware bias creates a persistent error floor that standard averaging cannot correct. To overcome this limitation, we propose Q-ANCHOR, a quantum-aware federated aggregation architecture that anchors server updates with zero-noise extrapolation while applying stateful client correction to suppress both client drift and hardware-induced bias. Our convergence theory proves that Q-ANCHOR successfully mitigates classical client drift while actively reducing the hardware-bias floor. Experimental results demonstrate that Q-ANCHOR achieves significantly more stable training than conventional FL baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims that FedAvg in quantum federated learning exhibits a persistent error floor under combined non-IID client drift and hardware bias from noisy quantum gradient estimates. It proposes the Q-ANCHOR architecture, which applies zero-noise extrapolation (ZNE) to anchor server-side updates together with stateful client correction, and asserts a convergence theory proving that this mitigates client drift while actively reducing the hardware-bias floor. Experiments are stated to show more stable training than standard FL baselines.

Significance. If the convergence analysis is rigorous and the ZNE mechanism is shown to be implementable without additional unstated assumptions, the work would address a practically relevant barrier to deploying QFL on NISQ hardware. The explicit mathematical demonstration of FedAvg limitations under hardware noise would be a useful contribution if the derivation is independent and non-circular.

major comments (2)
  1. [Abstract] Abstract: the claim that 'our convergence theory proves that Q-ANCHOR successfully mitigates classical client drift while actively reducing the hardware-bias floor' supplies no equations, proof steps, or listed assumptions, preventing assessment of whether the bound on the bias-floor term is derived independently of the ZNE effectiveness or reduces to an oracle assumption on extrapolated updates.
  2. [Q-ANCHOR architecture description] Q-ANCHOR architecture description: server-side ZNE is presented as the mechanism that anchors updates and reduces hardware bias, yet ZNE requires multiple noise-scaled evaluations of the same observable (via gate folding or pulse stretching); the server receives only classical aggregates and the manuscript does not specify whether clients submit multi-noise runs per round or how a purely classical extrapolation rule is defined on averaged values, which is load-bearing for the claimed bias-floor reduction.
minor comments (1)
  1. [Abstract] The abstract references 'experimental results' demonstrating stability but provides no information on the quantum circuit model, noise model, number of clients, data partitioning, or quantitative metrics (e.g., test accuracy curves or bias-floor measurements).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major point below with clarifications drawn from the manuscript and indicate where revisions will strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'our convergence theory proves that Q-ANCHOR successfully mitigates classical client drift while actively reducing the hardware-bias floor' supplies no equations, proof steps, or listed assumptions, preventing assessment of whether the bound on the bias-floor term is derived independently of the ZNE effectiveness or reduces to an oracle assumption on extrapolated updates.

    Authors: The abstract is a concise summary; the full convergence analysis appears in Section 4. We model hardware bias as an additive, noise-dependent term in the quantum gradient estimates and derive an explicit bound showing that the bias-floor term contracts with the ZNE extrapolation order while the client-drift term is controlled separately by the stateful correction. The derivation is independent of any oracle assumption on the extrapolated values. We will revise the abstract to reference the key assumptions and point to Section 4. revision: yes

  2. Referee: [Q-ANCHOR architecture description] Q-ANCHOR architecture description: server-side ZNE is presented as the mechanism that anchors updates and reduces hardware bias, yet ZNE requires multiple noise-scaled evaluations of the same observable (via gate folding or pulse stretching); the server receives only classical aggregates and the manuscript does not specify whether clients submit multi-noise runs per round or how a purely classical extrapolation rule is defined on averaged values, which is load-bearing for the claimed bias-floor reduction.

    Authors: Section 3.1 states that clients execute multiple noise-scaled circuit evaluations (via gate folding) for each local gradient and transmit the resulting classical estimates; the server then applies a standard polynomial extrapolation to the received aggregates. This is a purely classical post-processing step. We will insert an explicit protocol description in Section 3 to remove any ambiguity. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract states that a convergence theory proves Q-ANCHOR mitigates client drift and reduces the hardware-bias floor via ZNE-guided anchoring, but contains no equations, derivations, or proof details that can be inspected for self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations. No specific step is shown to be equivalent to its inputs by construction. The architecture description and claims remain independent of any visible circular mechanism.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain assumption that hardware bias produces a persistent uncorrectable floor under standard averaging and that ZNE can be integrated into federated aggregation without new uncontrolled errors; no free parameters or invented physical entities are mentioned in the abstract.

axioms (1)
  • domain assumption Quantum hardware bias creates a persistent error floor that standard averaging cannot correct.
    Explicitly stated in the abstract as the motivation for moving beyond FedAvg.
invented entities (1)
  • Q-ANCHOR architecture no independent evidence
    purpose: Anchors server updates with ZNE and applies stateful client correction to suppress double-drift.
    Newly proposed method whose effectiveness is the load-bearing claim.

pith-pipeline@v0.9.1-grok · 5720 in / 1411 out tokens · 36386 ms · 2026-06-29T09:02:16.840921+00:00 · methodology

discussion (0)

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