Adversarial Effects on Expressibility and Trainability in Distributed Variational Quantum Algorithms

2026-05-05

AI Summary

This work addresses the vulnerability of entangling layers shared across processors in distributed variational quantum algorithms to adversarial perturbations, which degrade both expressibility and trainability. The authors propose a Kraus-operator-based measure of expressibility, establish its trade-off with the trainability of noisy circuits, and model the mapping from entanglement perturbations to structured gate noise. Through gradient variance analysis and numerical simulations, they demonstrate that adversarial perturbations can systematically steer optimization trajectories toward incorrect solutions—even while avoiding barren plateaus—thereby significantly impairing learning performance. This study provides the first mechanistic explanation of how adversarial manipulation compromises quantum optimization and lays a theoretical foundation for robust distributed quantum learning.

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.

Problem

• adversarial perturbations
• distributed variational quantum algorithms
• entanglement sharing
• expressibility
• trainability

Innovation

• Kraus expressibility
• adversarial perturbations
• distributed variational quantum algorithms
• trainability
• entanglement vulnerability