Does anyone know of a direct quantum algorithm for computing GCD, - There could be quantum gates for addition subtraction constructed explicitly, using CNOT, etc. - the construction can be done in some poly(n) of input, (this is just a guess), but is there any algorithm, scheme for computing GCD, using quantum algorithms, gauss sums, QFT, quantum approximation, anything(!!) thanks,
A search for "Quantum GCD" yields a 2013 paper by Saeedi and Markov titled "Quantum Circuits for GCD Computation with O(n \log n) Depth and O(n) Ancillae". It's not mentioned in the title, but the size of the circuit used in their algorithm $O(n^2)$.