Illustration of Barren Plateaus in Quantum Computing

2026-02-18

AI Summary

This work investigates the impact of parameter sharing on the optimization landscape of variational quantum circuits. While parameter sharing reduces the dimensionality of trainable parameters, it introduces misleading gradients that exacerbate optimization challenges. The study proposes a novel framework to quantify the deceptiveness of gradients and the associated optimization difficulty. Through a combination of gradient analysis and systematic experiments, it establishes—for the first time—a quantitative relationship between the degree of parameter sharing and the complexity of the optimization landscape. Empirical results demonstrate that higher levels of parameter sharing lead to increasingly deceptive gradients, significantly degrading the performance of standard optimizers such as Adam and SGD and rendering them highly sensitive to hyperparameter choices.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Variational Quantum Circuits (VQCs) have emerged as a promising paradigm for quantum machine learning in the NISQ era. While parameter sharing in VQCs can reduce the parameter space dimensionality and potentially mitigate the barren plateau phenomenon, it introduces a complex trade-off that has been largely overlooked. This paper investigates how parameter sharing, despite creating better global optima with fewer parameters, fundamentally alters the optimization landscape through deceptive gradients -- regions where gradient information exists but systematically misleads optimizers away from global optima. Through systematic experimental analysis, we demonstrate that increasing degrees of parameter sharing generate more complex solution landscapes with heightened gradient magnitudes and measurably higher deceptiveness ratios. Our findings reveal that traditional gradient-based optimizers (Adam, SGD) show progressively degraded convergence as parameter sharing increases, with performance heavily dependent on hyperparameter selection. We introduce a novel gradient deceptiveness detection algorithm and a quantitative framework for measuring optimization difficulty in quantum circuits, establishing that while parameter sharing can improve circuit expressivity by orders of magnitude, this comes at the cost of significantly increased landscape deceptiveness. These insights provide important considerations for quantum circuit design in practical applications, highlighting the fundamental mismatch between classical optimization strategies and quantum parameter landscapes shaped by parameter sharing.

Problem

• Barren Plateaus
• Variational Quantum Circuits
• Parameter Sharing
• Gradient Deceptiveness
• Quantum Optimization

Innovation

• parameter sharing
• barren plateaus
• deceptive gradients
• variational quantum circuits
• optimization landscape