Shaping Expressibility in Variational Circuits: Balancing Trainability and Performance through Experimental Analysis

Abstract

Variational Quantum Circuits (VQCs) are a cornerstone of Quantum Machine Learning (QML), offering flexible quantum models that can be optimized for a variety of tasks. However, the expressibility and trainability of these circuits often present conflicting design chal- lenges, particularly in the presence of barren plateaus that hinder op- timization. This work investigates two techniques—bandwidth tuning and latent qubits—as mechanisms to shape the expressibility of VQCs to increase trainability or allow circuits to reach parameter combina- tions that better fit the problem. We conduct an extensive experimental study using quantum classifiers, systematically analyzing the impact of these techniques on key performance metrics, including expressibility, loss dispersion, and completeness. Our results confirm that bandwidth tuning does not significantly increase trainability while considerably re- ducing expressiveness, making it unsuitable for quantum neural networks (QNNs). Conversely, latent qubits enhance trainability and the best pos- sible results in already trainable circuits by expanding the quantum fea- ture space with minimal loss of expressiveness, albeit with diminishing returns as the number of qubits increases. These findings provide insights into the applicability of these techniques to QNNs, with implications for the design of scalable hybrid quantum-classical algorithms.