Decompositions of multiple controlled-Z gates on various qubit-coupling graphs

Efficient decomposition of multiqubit operators is critical in the execution of quantum algorithms. In this paper, we introduce decompositions of the multiple controlled-Z (CCZ and CCCZ) gates tailored to various qubitcoupling graphs. Specifically, we demonstrate that the CCZ gate is realized with CZ-depth 4 on a square-shaped qubit-coupling graph utilizing one auxiliary qubit. As for the CCCZ gate, previous research indicated that the decomposition requires 14 CZ gates in a fully connected topology. However, our findings reveal that only four specific qubit couplings are needed to achieve a decomposition using the same number of CZ gates, 14. Our research employs an optimization method to improve the alignment of parametrized quantum circuits with their intended quantum gates, which facilitates these efficient decompositions. This methodology is versatile and can be applied to decompose any quantum gates, not just the CCZ and CCCZ gates. These advancements in decomposing multiqubit gates, coupled with our CCZ and CCCZ decompositions, are poised to reduce quantum circuit execution times and enhance the efficiency of complex quantum algorithms in imminent quantum computing applications.