Alternating ZX Circuit Extraction for Hardware-Adaptive Compilation

We present a novel quantum circuit extraction scheme that tightly integrates graph-like ZX diagrams with hardware-adaptive routing. The method utilizes the degrees of freedom during the conversion from a ZX diagram to a quantum circuit (extraction). It alternates between generating multiple extraction options and evaluating them based on hardware constraints, allowing the routing algorithm to inform and guide the extraction process. This feedback loop extends existing graph-like ZX extraction and supports modular integration of different extraction algorithms, routing strategies, and target hardware, making it a versatile building block during compilation. To perform numerical evaluations, a reference instance of the scheme is implemented with SWAP-based routing for neutral atom hardware and evaluated using various benchmark collections on small-to mid-scale circuits. The reference code is available as open-source, allowing fast integration of other extraction and/or routing tools to stimulate further research and foster improvements of the proposed scheme.