攻击共享纠缠会破坏分布式量子算法的表达能力与训练性。
Adversarial Effects on Expressibility and Trainability in Distributed Variational Quantum Algorithms
- 通过克劳斯表示将纠缠扰动映射为门级噪声
- 发现噪声电路存在表达能力与可训练性的权衡
- 适合研究量子对抗攻击或分布式量子优化的学者
分布式量子算法为突破噪声中等规模量子硬件限制提供了可行路径。然而，现有方法隐含假设量子处理器间的纠缠共享层是可信的。本文揭示这一假设带来根本性漏洞：对手对共享纠缠施加扰动，会产生结构化门级噪声，直接影响量子学习性能。我们构建了通过显式克劳斯表示将纠缠级扰动映射至门级噪声的框架。为量化影响，提出克劳斯表达能力（Kraus expressibility）——一种推广至噪声量子通道的酉表达能力度量。通过梯度方差分析，建立克劳斯表达能力与噪声电路可训练性之间的权衡关系。分析表明，对手可操纵克劳斯表达能力，在避免梯度消失（避开平坦区）的同时系统性引导优化走向错误解。数值模拟验证了表达能力与可训练性的对抗退化现象。
原文摘要 · Abstract (English)
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.
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