  We devise greedy heuristics tailored for synthesizing quantum circuits that
implement a specified set of Pauli rotations. Our heuristics are designed to
minimize either the count of entangling gates or the depth of entangling gates,
and they can be adjusted to either maintain or loosen the ordering of
rotations. We present benchmark results demonstrating a depth reduction of up
to a factor of 4 compared to the current state-of-the-art heuristics for
synthesizing Hamiltonian simulation circuits. We also show that these
heuristics can be used to optimize generic quantum circuits by decomposing and
resynthesizing them.
