Is there a good comparison of alternative versions of the Quantum Fourier Transform (QFT) that mirror the alternative decimation-in-time or decimation in frequency versions for the conventional Fast Fourier Transform (FFT)?
Most of the descriptions that I find seem to be based on Nielsen and Chuang's text, which appears to be based on the decimation in frequency version: the input qubits are in regular order and the output qubits are in bit-reversed order.
The recursive construction presented in the text "Quantum Computing: A Gentle Introduction," by Eleanor Rieffel and Wolfgang Polak, appears to be based on a decimation in time version, where, once the recursion is rolled out, the input qubits will first be sorted in bit reversed order before performing the rest of the transform.
Partly, related to the above, I also have a question regarding drawing conventions for quantum circuits. In a large part of the world, we read from left to right and top to bottom. Therefore, if one is using the little-endian ordering with the lowest order qubit in the rightmost position for horizontal placement , I would expect vertical placement to use a convention with the lowest order qubit in the bottom-most position. However, almost all the circuit diagrams I see for the QFT seem to have the lowest order qubit in the top-most position (and other circuit diagrams do not necessarily follow a consistent convention). I'd appreciate any insight into why this is the case.