Illustration of Barren Plateaus in Quantum Computing

TL;DR

This paper explores how parameter sharing in variational quantum circuits affects the optimization landscape, revealing increased deceptiveness and challenges for gradient-based optimizers, with implications for quantum circuit design.

Contribution

It introduces a framework to measure landscape deceptiveness and demonstrates the trade-offs of parameter sharing in quantum circuit optimization.

Findings

Parameter sharing increases landscape deceptiveness.

Gradient-based optimizers' performance degrades with more sharing.

A new deceptiveness detection algorithm was developed.

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.