On the constant depth implementation of Pauli exponentials

Abstract We decompose, under the very restrictive linear nearest-neighbour connectivity, Z ⊗ n exponentials of arbitrary length into circuits of constant depth using $${\mathcal{O}}(n)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> ancillae and two-body XX and ZZ interactions. Consequently, a similar method works for arbitrary P