Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates

We show how to efficiently decompose a parameterized multi-qubit Pauli (PMQP) gate into native parameterized two-qubit Pauli (P2QP) gates minimizing both the circuit depth and the number of P2QP gates. Given a realistic quantum computational model, we argue that the technique is optimal in terms of the number of hardware native gates and the overall depth of the decomposition. Starting from PMQP gate decompositions for the path and star hardware graph, we generalize the procedure to any generic hardware graph and provide exact expressions for the depth and number of P2QP gates of the decomposition. Furthermore, we show how to efficiently combine the decomposition of multiple PMQP gates to further reduce the depth as well as the number of P2QP gates for a combinatorial optimization problem using the Lechner-Hauke-Zoller (LHZ) mapping.