A highly-effective quantum program compilation framework targeting SU(4) gate set

A quantum compiler translates high-level program semantics into quantum gates from a universal gate set, typically composed of only single-qubit (1Q) and two-qubit (2Q) native operations. Different gate sets can result in varying performance outcomes. Continuous gate sets, like fSim and XY families, offer higher expressiveness than the commonly used CX-based set, but they present critical challenges particularly in calibration overhead and native compilation strategies. Thus, CX-based gate sets and their companion state-of-the-art (SOTA) compilers remain dominant. Recent work has shown that arbitrary 2Q gates can be directly implemented on quantum processors. We propose using the entire SU(4) group as the native gate set for maximum expressiveness. We developed an end-to-end compiler tailored to the SU(4) gate set, integrating high-level program synthesis, local circuit optimization, and qubit mapping to output directly executable circuits. Experimental results show that our compiler significantly reduces 2Q gate count and circuit depth compared to SOTA CX-based compilers across various benchmarks, while maintaining manageable calibration costs and minimizing 2Q gate overhead during qubit mapping. Our work not only tackles the challenges of using a continuous gate set but also redefines key problems in quantum program compilation.