Parametric quantum circuits play a crucial role in the performance of many variational quantum algorithms. To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution space while maintaining a low parameter count and circuit depth. In this paper, we develop a method to analyze the dimensional expressivity of parametric quantum circuits. Our technique allows for identifying superfluous parameters in the circuit layout and for obtaining a maximally expressive ansatz with a minimum number of parameters. Using a hybrid quantum-classical approach, we show how to efficiently implement the expressivity analysis using quantum hardware, and we provide a proof of principle demonstration of this procedure on IBM's quantum hardware. We also discuss the effect of symmetries and demonstrate how to incorporate or remove symmetries from the parametrized ansatz.
@article{arxiv.2011.03532,
title = {Dimensional Expressivity Analysis of Parametric Quantum Circuits},
author = {Lena Funcke and Tobias Hartung and Karl Jansen and Stefan Kühn and Paolo Stornati},
journal= {arXiv preprint arXiv:2011.03532},
year = {2021}
}