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In this paper, we investigate how quantum architectures affect the efficiencyof the execution of the quantum Fourier transform (QFT) and lineartransformations, which are essential parts of the stabilizer/Clifford groupcircuits. In particular, we show that in most common and realistic physicalarchitectures including the linear nearest neighbor, two-dimensional lattice,and bounded degree graph (containing a chain of length n), n-qubit QFT andn-qubit stabilizer circuits can be parallelized to linear depth using noauxiliary qubits. We construct lower bounds that show the efficiency of ourapproach.Comment: 8 pages, 6 figures. Extended discussions, improved presentatio

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