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arXiv · 2408.08265

On the Constant Depth Implementation of Pauli Exponentials

Ioana Moflic·Alexandru Paler
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Abstract

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.

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Ioana Moflic, Alexandru Paler. 2024-08-15. On the Constant Depth Implementation of Pauli Exponentials. https://doi.org/10.1038/s41534-026-01226-x

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