cs.LGFeb 18, 2026

Illustration of Barren Plateaus in Quantum Computing

Authors: Gerhard Stenzel, Tobias Rohe, Michael Kölle, Leo Sünkel, Jonas Stein, Claudia Linnhoff-Popien

Organizations: LMU Munich

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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 & tables

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.
Figure 6: Distribution of the minimal loss of the SGD optimizer measured during each run for different parameter sharing applications and learning rates, compared to the global minimum and deceptiveness ratio.
Figure 7: Minimal loss of the Adam and SGD optimizers measured during each run for different parameter sharing applications and learning rates, compared to the global minimum and deceptiveness ratio.
Figure 8: Stability of deceptiveness metrics across varying resolutions persists in quantum systems with increasing qubit counts.
Figure 9: Empirical distribution of gradient magnitudes across varying resolution configurations for a two-qubit quantum circuit. The observed scaling behavior aligns with theoretical predictions outlined in section 3.1 , except the lowest resolution configuration (90 sample points), depicted in blue.
Figure 10: Loss of the Adam and SGD optimizers at the last epoch for different parameter sharing applications and learning rates, compared to the global minimum.

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