# Adversarial Effects on Expressibility and Trainability in Distributed Variational Quantum Algorithms

arXiv: https://arxiv.org/abs/2605.03629 · HTML: https://mlsanity.com/paper/2605.03629/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 75 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 19 of 19)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search](https://mlsanity.com/paper/2406.17630/) (2024)
- [Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines](https://mlsanity.com/paper/2207.05865/) (2022)
- [High Dimensional Quantum Machine Learning With Small Quantum Computers](https://mlsanity.com/paper/2203.13739/) (2022)
- [A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models](https://mlsanity.com/paper/2303.15626/) (2023)
- [Generative quantum advantage for classical and quantum problems](https://mlsanity.com/paper/2509.09033/) (2025)
- [QuantumLeak: Stealing Quantum Neural Networks from Cloud-based NISQ Machines](https://mlsanity.com/paper/2403.10790/) (2024)
- [Reinforcement learning with learned gadgets to tackle hard quantum problems on real hardware](https://mlsanity.com/paper/2411.00230/) (2024)
- [Security Attacks Abusing Pulse-level Quantum Circuits](https://mlsanity.com/paper/2406.05941/) (2024)
- [Distributed Quantum Computing and Network Control for Accelerated VQE](https://mlsanity.com/paper/2101.02504/) (2021)
- [AI-driven Reverse Engineering of QML Models](https://mlsanity.com/paper/2408.16929/) (2024)
- [Accelerating variational quantum algorithms with multiple quantum processors](https://mlsanity.com/paper/2106.12819/) (2021)
- [OPAQUE: Obfuscating Phase in Quantum Circuit Compilation for Efficient IP Protection](https://mlsanity.com/paper/2502.16605/) (2025)
- [CopyQNN: Quantum Neural Network Extraction Attack under Varying Quantum Noise](https://mlsanity.com/paper/2504.00366/) (2025)
- [Practical limitations on robustness and scalability of quantum Internet](https://mlsanity.com/paper/2308.12739/) (2023)

## Abstract (arXiv)

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.