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.
I. INTRODUCTIONFurther accelerating the speed of scientific progress requires computational resources beyond the capabilities of state-of-the-art classical computing. Computational power has been growing exponentially for a couple of decades according to Moore's law. However, the miniaturisation of classical computers has reached hard physical boundaries bringing Moore's Law to an end. In recent years, Quantum Computing (QC) has emerged as a promising alternative [1, 2] that could provide exponentially growing compute power for application areas like quantum chemistry, optimisation and machine learning. Quantum algorithms, including speedup proofs, have been developed within all these application areas.High-level quantum algorithms using arbitrary quantum gates need to be mapped to hardware native gates. This mapping often leads to an overhead in terms of the number of gates due to non-local and multi-qubit gates. For example, fermion-to-qubit mappings, like the Jordan-Wigner transformation [3] and others [4][5][6] necessitate parameterized gates acting on more than