Dimensional Expressivity Analysis of Parametric Quantum Circuits

• URL: http://arxiv.org/abs/2011.03532v4
• Date: Tue, 4 May 2021 14:31:03 GMT
• Title: Dimensional Expressivity Analysis of Parametric Quantum Circuits
• Authors: Lena Funcke, Tobias Hartung, Karl Jansen, Stefan K\"uhn, Paolo Stornati
• Abstract summary: We show how to efficiently implement the expressivity analysis using quantum hardware. We also discuss the effect of symmetries and demonstrate how to incorporate or remove symmetries from the parametrized ansatz.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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