A greedy transpilation strategy for quantum circuit optimization of Pauli gadgets

For near-term quantum computing experiments, reducing multi-qubit gate costs is critical for efficient and accurate simulations. A common primitive within physical simulations are exponentials of Pauli operators (or Pauli gadgets), which can generate all unitary operators. Known decompositions exist but involve many multi-qubit gates for each Pauli gadget. While current transpilers can exactly reduce arbitrary 1- and 2-qubit unitaries, they struggle with larger unitary operators. We present a greedy strategy for transpilation of generic Pauli exponentials, utilizing tableau and circuit-based representations to efficiently decompose commuting and non-commuting series of Pauli gadgets. We benchmark our strategy against existing approaches such as phase polynomial synthesis with Pauli gadget sequences as well as practical exponential ansatz structures from quantum chemistry.