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In this paper we improve the layered implementation of arbitrary stabilizercircuits introduced by Aaronson and Gottesman in {\it Phys. Rev. A 70(052328)},2004. In particular, we reduce their 11-stage computation-H-C-P-C-P-C-H-P-C-P-C- into an 8-stage computation of the form-H-C-CZ-P-H-P-CZ-C-. We show arguments in support of using -CZ- stages over the-C- stages: not only the use of -CZ- stages allows a shorter layeredexpression, but -CZ- stages are simpler and appear to be easier to implementcompared to the -C- stages. Relying on the 8-stage decomposition we develop atwo-qubit depth-$(14n-4)$ implementation of stabilizer circuits over the gatelibrary {P,H,CNOT}, executable in the LNN architecture, improving bestpreviously known depth-$25n$ circuit, also executable in the LNN architecture.Our constructions rely on folding arbitrarily long sequences $($-P-C-$)^m$ intoa 3-stage computation -P-CZ-C-, as well as efficient implementation of the -CZ-stage circuits.

Optimized Aaronson-Gottesman stabilizer circuit simulation through quantum circuit transformations