Can you tell if my idea to solve the problems isomorphic to the HSP of nonabelian groups has future?

Can you tell if my idea to solve the problems isomorphic to the HSP of nonabelian groups has future? Ask Question Asked 3 days ago Modified 3 days ago Viewed 48 times 1 When you solve lets say the period finding algorithm , you need to prepare the state of qubits into a superposition of states 0 and 1.And this is what the Hadamard gate does before you put it into the oracle and QFT or whatever. However I always wondered , why the need for equal amplitudes in the superposition of those qubits.The Hadamard gate puts the qubits into equal amplitude supeposition of all qubits in a quantum algorithm but why would that neccesarly work for all problems? One of the problems in solving the HSP for nonabellian groups is frequency mixing from the 2d irreps (or higher order irreps) which are present in nonabellian groups.If you had a ready state of 1 2 √ (1,1 ) T 1 2 ( 1 , 1 ) 𝑇 before the oracle and the QFT for such a nonabellian group due to frequency mixing there doesnt seem to be cancellation of irrelevant frequencies in the QFT but lets say you had any other superposition of |0> and |1> before the oracle and the QFT for a nonabellian group ,wouldnt that possibly cancel out some of the unwanted frequencies after the QFT? Has there been any reasearch on this,have I said something wrong and is it worth pursuing?thanks. quantum-algorithmsquantum-fourier-transform Share Improve this question Follow asked Jul 21 at 12:25 Root Groves 1658 8 bronze badges I seem to remember this was part of the motivation for looking at Schur and Clebsch-Gordan Transforms... –  DaftWullie Commented Jul 21 at 12:48 You might also like to look up the HHL algorithm. One of the optimisations they make is instead of providing the uniform superposition as input, they tweak it to optimise the error probability for their specific use case. Not exactly what you're asking, but is an example where changing the input state helps. –  DaftWullie Commented Jul 21 at 14:34 Add a comment Know someone who can answer? Share a link to this question via email, Twitter, or Facebook. 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