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arxiv: 2605.03629 · v1 · submitted 2026-05-05 · 🪐 quant-ph · cs.LG

Recognition: unknown

Adversarial Effects on Expressibility and Trainability in Distributed Variational Quantum Algorithms

Abhishek Sadhu , Sharu Theresa Jose
Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:01 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG
keywords distributed quantum computingvariational quantum algorithmsadversarial attacksKraus operatorsexpressibilitytrainabilitybarren plateausquantum noise
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The pith

An adversary can perturb shared entanglement to keep gradients large in distributed variational quantum algorithms while biasing results to incorrect solutions.

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

Distributed variational quantum algorithms assume a trusted layer for sharing entanglement across separate quantum processors to enable larger computations. The paper demonstrates that this assumption creates an opening for adversaries to inject perturbations into the shared entanglement. These perturbations translate into structured noise at the level of quantum gates through an explicit mapping. The authors introduce Kraus expressibility as a way to measure the impact on the circuit's ability to represent quantum states and analyze how it relates to the size of cost gradients during training. Their key finding is that an adversary can tune this metric to preserve usable gradients and thereby avoid barren plateaus, yet still steer the optimization process toward wrong answers.

Core claim

By constructing an explicit Kraus representation that converts entanglement-level perturbations into equivalent gate-level noise, the paper shows that an adversary can adjust Kraus expressibility so that the variance of the cost-function gradients remains large enough to avoid barren plateaus while the same perturbations systematically shift the landscape toward incorrect solutions that the variational optimizer will converge to.

What carries the argument

Kraus expressibility, a metric that extends the notion of unitary expressibility to noisy channels and is used to relate entanglement perturbations to the trainability of the variational circuit through gradient-variance calculations.

If this is right

  • Adversarial perturbations of shared entanglement can preserve sufficiently large cost gradients to avoid barren plateaus during training of distributed variational circuits.
  • The same perturbations can introduce a directional bias that causes the optimizer to converge to incorrect rather than optimal solutions.
  • The trade-off between Kraus expressibility and gradient variance allows an adversary to maintain trainability while degrading solution quality.
  • Distributed variational algorithms therefore depend on the security of the entanglement-sharing layer to reach correct answers.

Where Pith is reading between the lines

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

  • Quantum networks that distribute entanglement for computation may need authentication or verification steps at the entanglement source to prevent these attacks.
  • The vulnerability could appear in other distributed quantum tasks that rely on shared entanglement, such as sensing or simulation protocols.
  • Mitigation approaches might include local verification of entanglement quality or redesign of the variational ansatz to reduce sensitivity to this class of noise.

Load-bearing premise

The explicit Kraus representation accurately maps arbitrary entanglement-level perturbations to gate-level noise without unaccounted-for effects from the physical entanglement distribution channel.

What would settle it

Numerical simulations in which controlled perturbations are applied to the shared entanglement and the optimization trajectory is observed to converge to a demonstrably incorrect solution while the measured gradient norms stay above the scale expected for barren plateaus.

Figures

Figures reproduced from arXiv: 2605.03629 by Abhishek Sadhu, Sharu Theresa Jose.

Figure 1
Figure 1. Figure 1: (a) Distributed VQAs under adversarial influence: A strong adversary corrupts shared en￾tanglement among the network nodes, while a weak adversary injects local noise at QPUs, disrupting optimization. (b) Kraus expressiblity and solution coverage: Let SA and SB denote solution sets within the unitary group for problems A and B. Adversarially-induced noisy non-local gates restrict the accessible transformat… view at source ↗
Figure 2
Figure 2. Figure 2: Impact of adversarial perturbations on VQE view at source ↗
Figure 3
Figure 3. Figure 3: Adversarial impact on trainability for n = 6 qubit systems. (a) For fixed trainable parameters, Kraus expressibility norm decays with PQCh-ansatz depth and adversarial noise. (b) Adversarial noise in non-local CNOTs (via reduced concurrence) renders even shallow circuits untrainable. (c) At fixed depth, stronger adversarial noise (low concurrence) reduces gradient variance thereby impeding optimization. Th… view at source ↗
Figure 4
Figure 4. Figure 4: Scaling of the cost-function gradient variance with the number of qubits view at source ↗
read the original abstract

Distributed quantum algorithms offer a promising pathway to scale variational quantum algorithms beyond the constraints of noisy intermediate-scale quantum hardware. However, existing approaches implicitly assume a trusted entanglement-sharing layer across quantum processors. We show that this assumption introduces a fundamental vulnerability: adversarial perturbations of shared entanglement induce structured gate-level noise that directly impacts quantum learning. We develop a framework that maps entanglement-level perturbations to gate-level noise via an explicit Kraus representation. To quantify their impact, we introduce Kraus expressibility, a metric that generalizes unitary expressibility to noisy quantum channels. We then establish a trade-off between Kraus expressibility and trainability of noisy quantum circuits through gradient variance analysis. Our analysis reveals that an adversary can manipulate Kraus expressibility to maintain sufficiently large cost gradients (avoiding barren plateaus) while systematically biasing optimization toward incorrect solutions. We validate these findings through numerical simulations, demonstrating adversarial degradation of expressibility and trainability.

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 / 2 minor

Summary. The manuscript presents a framework for analyzing adversarial effects in distributed variational quantum algorithms (VQAs). It maps entanglement-level perturbations to gate-level noise using an explicit Kraus representation, introduces a new metric called 'Kraus expressibility' that generalizes unitary expressibility to noisy channels, establishes a trade-off between this expressibility and trainability via gradient variance analysis, and shows that an adversary can maintain large cost gradients while biasing the optimization toward incorrect solutions. These findings are supported by numerical simulations demonstrating degradation in expressibility and trainability.

Significance. If the central claims hold, this work is significant for highlighting a critical vulnerability in the trusted entanglement-sharing assumption in distributed quantum computing. The introduction of Kraus expressibility offers a novel tool for assessing noisy quantum channels in variational learning settings. The gradient variance analysis provides insights into avoiding barren plateaus while introducing bias, which could guide the development of more robust distributed VQAs. The numerical validation adds practical relevance, though additional details on statistical robustness would enhance its impact.

major comments (2)
  1. [Framework and Kraus mapping] The explicit Kraus representation (abstract and framework section) is the sole bridge between entanglement perturbations and the claimed structured gate noise that preserves gradient variance while enabling bias. However, it may omit non-unitary physical effects from the entanglement distribution channel (e.g., photon loss, timing jitter, mode mismatch), so the effective noise seen by the variational circuit could differ from the modeled Kraus channel, weakening the central trade-off claim.
  2. [Numerical simulations] Numerical validation (validation section) is cited to support the adversarial degradation of expressibility and trainability, but lacks visible error bars, full derivation steps for the gradient variance analysis, or data exclusion details. Since the claim of controlled bias while preserving gradients rests on these unverified steps, the evidence is insufficient to confirm the trade-off.
minor comments (2)
  1. [Abstract] The abstract is concise but could briefly note the circuit sizes or depths used in the numerical examples to provide immediate context for the validation results.
  2. [Metric definition] Ensure the definition of Kraus expressibility is explicitly cross-referenced upon first use and compared directly to standard unitary expressibility to clarify the generalization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We address each of the major comments below and outline the revisions we will make to improve the clarity and robustness of our results.

read point-by-point responses

  1. Referee: The explicit Kraus representation (abstract and framework section) is the sole bridge between entanglement perturbations and the claimed structured gate noise that preserves gradient variance while enabling bias. However, it may omit non-unitary physical effects from the entanglement distribution channel (e.g., photon loss, timing jitter, mode mismatch), so the effective noise seen by the variational circuit could differ from the modeled Kraus channel, weakening the central trade-off claim.

    Authors: We acknowledge that our Kraus representation focuses on modeling the adversarial perturbations to the shared entanglement and does not encompass all possible non-unitary effects that may occur in physical entanglement distribution channels. Our central claim is that within this modeled framework, an adversary can exploit the structure to maintain gradient variance while introducing bias. To strengthen the manuscript, we will add a paragraph in the framework section discussing the assumptions of the model and noting that additional physical effects could be incorporated as further noise channels in extensions of this work. This clarification will help contextualize the applicability of our results. revision: partial

  2. Referee: Numerical validation (validation section) is cited to support the adversarial degradation of expressibility and trainability, but lacks visible error bars, full derivation steps for the gradient variance analysis, or data exclusion details. Since the claim of controlled bias while preserving gradients rests on these unverified steps, the evidence is insufficient to confirm the trade-off.

    Authors: We agree that providing more details on the numerical simulations will enhance the credibility of our findings. In the revised version, we will include error bars in the figures of the validation section, calculated from repeated simulations with different random seeds. We will also append the complete derivation of the gradient variance analysis to the supplementary material and explicitly describe the criteria for any data exclusion or averaging procedures used. These changes will allow readers to fully verify the reported trade-off. revision: yes

Circularity Check

0 steps flagged

No significant circularity; new metrics and mappings are independently defined

full rationale

The paper's core chain introduces an explicit Kraus representation to map entanglement perturbations to gate noise, defines Kraus expressibility as a generalization of unitary expressibility, and derives the expressibility-trainability trade-off via gradient variance analysis. None of these steps reduce by construction to prior fitted values, self-citations, or renamed inputs; the adversarial bias claim follows from the new definitions and numerical validation rather than tautological equivalence. The derivation remains self-contained against external quantum channel and variational algorithm benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claims rest on standard quantum channel formalism plus the newly introduced Kraus expressibility metric; no explicit free parameters are stated in the abstract, and the mapping from entanglement perturbations is presented as direct.

axioms (2)
  • standard math Standard quantum channel theory and Kraus operator formalism apply to noise induced by entanglement perturbations.
    Invoked to develop the explicit mapping from entanglement-level perturbations to gate-level noise.
  • domain assumption Gradient variance analysis extends directly to noisy quantum channels for assessing trainability.
    Basis for establishing the expressibility-trainability trade-off under adversarial control.
invented entities (1)
  • Kraus expressibility no independent evidence
    purpose: Metric that generalizes unitary expressibility to quantify the effect of noisy channels on the range of representable operations.
    Newly defined in the paper to analyze adversarial impact on expressibility.

pith-pipeline@v0.9.0 · 5451 in / 1363 out tokens · 72508 ms · 2026-05-07T17:01:34.311733+00:00 · methodology

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