Illustration of Barren Plateaus in Quantum Computing

TL;DR

This paper investigates how parameter sharing in variational quantum circuits affects trainability by introducing deceptiveness in gradient information. It combines a gradient-deceptiveness detection algorithm with a quantitative framework to measure optimization difficulty, and analyzes optimizer performance under varying sharing degrees. The major finding is that while parameter sharing can dramatically improve expressivity and push global minima to better values, it also creates more deceptive landscapes, increasing gradient magnitudes and reducing the effectiveness of gradient-based optimizers like Adam and SGD, with success rates highly sensitive to hyperparameters. The results highlight a fundamental mismatch between classical optimization strategies and quantum parameter landscapes, and suggest directions such as gradient-free or hybrid optimization and adaptive sharing to balance expressivity and trainability in practical quantum circuits.

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.

Figures (10)

• Figure 1: Lower resolutions create scaling gradient magnitudes, shifting the distribution of gradients consistently.
• Figure 2: Lower resolutions create roughly the same deceptiveness.
• Figure 3: The default circuit used in our experiments.
• Figure 4: Exemplary run of circuit deceptiveness at different parameter sharing applications.
• Figure 5: Different trajectories of the Adam optimizer on the default circuit with different parameter sharing applications and learning rates.