On the Constant Depth Implementation of Pauli Exponentials

• URL: http://arxiv.org/abs/2408.08265v5
• Date: Wed, 20 Nov 2024 15:32:22 GMT
• Title: On the Constant Depth Implementation of Pauli Exponentials
• Authors: Ioana Moflic, Alexandru Paler,
• Abstract summary: We decompose arbitrary exponentials into circuits of constant depth using $mathcalO(n)$ ancillae and two-body XX and ZZ interactions. We prove the correctness of our approach, after introducing novel rewrite rules for circuits which benefit from qubit recycling.
• Score: 49.48516314472825
• License:
• Abstract: We decompose for the first time, under the very restrictive linear nearest-neighbour connectivity, $Z\otimes Z \ldots \otimes Z$ 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 fault-tolerant lattice surgery computations, to expressing arbitrary stabilizer circuits via two-body interactions only, parallel decoding of quantum error-correcting computations and to reducing the depth of NISQ computations, such as VQE.

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