On the Constant Depth Implementation of Pauli Exponentials

TL;DR

This paper presents a method to implement arbitrary Pauli exponential operators in constant depth circuits under linear nearest-neighbour connectivity, using ancillae and two-body interactions, with broad applications in quantum computing.

Contribution

It introduces a novel circuit decomposition technique for Pauli exponentials that is correct and efficient under restrictive connectivity constraints.

Findings

Achieves constant depth implementation of Pauli exponentials

Uses lgebraic rewrite rules and qubit recycling

Applicable to fault-tolerant quantum computations

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.