Classical simulation of quantum circuits is a pivotal part of the quantum computing landscape, specially within the NISQ era, where the constraints imposed by available hardware are unavoidable. The Gottesman-Knill theorem further motivates this argument by accentuating the importance of Clifford circuits and their role on this topic of simulation. In this work, we propose and analyze use cases that come from quantum circuits that can be written as product between a Clifford and a Non-Clifford unitary, these ranging from fully classical emulation, hybrid quantum-classical execution or even quantum algorithm simplification. To further complement this analysis, we make use of ZX-Calculus and its assets to detect a limiting border of these circuits that would allow for a separation between a Clifford section and a Non-Clifford section. To achieve this, we present a novel procedure for parsing ZX diagrams, that not only allows for the detection of this border but also simplifies the circuit extraction process.
Lima et al. (Tue,) studied this question.