  In this paper, we investigate how quantum architectures affect the efficiency
of the execution of the quantum Fourier transform (QFT) and linear
transformations, which are essential parts of the stabilizer/Clifford group
circuits. In particular, we show that in most common and realistic physical
architectures including the linear nearest neighbor, two-dimensional lattice,
and bounded degree graph (containing a chain of length n), n-qubit QFT and
n-qubit stabilizer circuits can be parallelized to linear depth using no
auxiliary qubits. We construct lower bounds that show the efficiency of our
approach.
