We decompose, under the very restrictive linear nearest-neighbour connectivity, Z⊗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 that 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.
