A 12-CNOT Double Qubit Excitation Gate

In this work, we presented, to the best of our knowledge, the first reported 12-CNOT decomposition of the double qubit excitation operator. We compared our new circuit with the previous SOTA 13-CNOT circuits in 4 different metrics. Our new circuit has the lowest CNOT count (12), lowest CNOT depth (8, roughly 27% reduction), and lowest total circuit depth (15, 25% reduction) among all the previous SOTA circuits. Further, we only added 2 extra one-qubit gates compared to the lowest one-qubit gate count (11) among the previous SOTA circuits. As the double qubit excitation operator can be used as a building block hundreds or thousands of times in practical quantum algorithms, any reduction in such primitives compounds over the full circuit, resulting in significant overall resource savings.