A quantum circuit parameterized decomposition method based on local synthesis

To reduce the number of basis gates after quantum circuit decomposition, enhance overall fidelity, and improve the expressivity of complex quantum programs, this paper proposes a quantum circuit parameterized decomposition method based on local synthesis (PDBLS). Prior to decomposition, local synthesis is applied to analyze and optimize the circuit structure by formally defining and automatically collecting “compressible blocks”, while also generating new compressible blocks through gate-exchange reordering, thereby reducing the number of basis gates requiring decomposition. At the theoretical level, within the Weyl chamber framework, we provide a rigorous proof showing that the optimal number of basis gates required for decomposing a two-qubit gate (2Q) corresponds exactly to the coverage layer in which its Weyl chamber coordinate lies. In the decomposition stage, we introduce a parameterized decomposition template alternating basis gates with U3 gates, combined with a cost function defined by decomposition fidelity and hardware fidelity, as well as a layer-by-layer deepening strategy with L-BFGS optimization, ensuring minimum basis gate usage while maintaining target fidelity. Experimental results demonstrate that PDBLS significantly reduces the number of 2Q basis gates across various benchmark circuits and gate sets, showing advantages under both exact and approximate decomposition conditions, and exhibiting strong scalability on large-scale circuits.