  Stabilizer circuits play an important role in quantum error correction
protocols, and will be vital for ensuring fault tolerance in future quantum
hardware. While stabilizer circuits are defined on the Clifford generating set,
{H, S, CX}, not all of these gates are native to quantum hardware. As such they
must be compiled into the native gateset, with the key difference across
hardware archetypes being the native two qubit gate. Here we introduce an
intuitive and accessible method for Clifford gate compilation. While multiple
open source solutions exist for quantum circuit compilation, these operate on
arbitrary quantum gates. By restricting ourselves to Clifford gates, the
compilation process becomes almost trivial and even large circuits can be
compiled manually. The core idea is well known: if two Clifford circuits
conjugate Paulis identically, they are equivalent. Compilation is then reduced
to ensuring that the instantaneous Pauli conjugation is correct for each qubit
at every timestep. This is Tableaux Manipulation, so called as we directly
interrogate stabilizer tableaux to ensure correct Pauli conjugation. We provide
a brief explanation of the process along with some worked examples to build
intuition; we finally show some comparisons for compiling large circuits to
open source software, and highlight that this method ensures a minimal number
of quantum gates are employed.
