Optimized Aaronson-Gottesman stabilizer circuit simulation through quantum circuit transformations

In this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004. In particular, we reduce their 11-stage computation -H-C-P-C-P-C-H-P-C-P-Cinto an 8-stage computation of the form -H-CCZ-P-H-P-CZ-C-. We show arguments in support of using -CZstages over the -Cstages: not only the use of -CZstages allows a shorter layered expression, but -CZstages are simpler and appear to be easier to implement compared to the -Cstages. Relying on the 8-stage decomposition we develop a two-qubit depth-(14n− 4) implementation of stabilizer circuits over the gate library {P,H,CNOT}, executable in the LNN architecture, improving best previously known depth-25n circuit, also executable in the LNN architecture. Our constructions rely on folding arbitrarily long sequences (-P-C-)m into a 3-stage computation -P-CZ-C-, as well as efficient implementation of the -CZstage circuits.