On the Constant Depth Implementation of Pauli Exponentials

We decompose, under the very restrictive linear nearest-neighbour connectivity, $Z^{\otimes n}$ exponentials of arbitrary length into circuits of constant depth using $\mathcal{O}(n)$ ancillae and two-body XX and ZZ interactions. Consequently, a similar method works for arbitrary Pauli exponentials. We prove the correctness of our approach, after introducing novel rewrite rules for circuits which benefit from qubit recycling. The decomposition has a wide variety of applications ranging from the efficient implementation of practical fault-tolerant lattice surgery computations, to expressing arbitrary stabilizer circuits via two-body interactions only and parallel decoding of quantum error-correcting computations.