Linear depth stabilizer and quantum Fourier transformation circuits with no auxiliary qubits in finite-neighbor quantum architectures

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 and 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.