Application of ZX-calculus to quantum architecture search

Abstract This paper presents a novel approach to quantum architecture search by integrating the techniques of ZX-calculus with Genetic Programming (GP) to optimize the structure of parameterized quantum circuits employed in quantum machine learning (QML). Recognizing the challenges in designing efficient quantum circuits for QML, we propose a GP framework that utilizes mutations defined via ZX-calculus, a graphical language that can simplify visualizing and working with quantum circuits. Our methodology focuses on evolving quantum circuits with the aim of enhancing their capability to approximate functions relevant in various machine learning tasks. We introduce several mutation operators inspired by the transformation rules of ZX-calculus and investigate their impact on the learning efficiency and accuracy of quantum circuits. The empirical analysis involves a comparative study where these mutations are applied to a diverse set of quantum regression problems, measuring performance metrics such as the percentage of valid circuits after the mutation, improvement of the objective, and circuit depth and width. Our results indicate that certain ZX-calculus-based mutations perform significantly better than others for quantum architecture search (QAS) in all metrics considered. They suggest that ZX-diagram-based QAS results in shallower circuits and more uniformly allocated gates than crude genetic optimization based on the circuit model. The code used for the numerical experiments is open source and can be found at TODO https://gitlab.cc-asp.fraunhofer.de/itwm-fm-qc-public/cvqa .