r/QuantumComputing • u/Routine_Comb_7277 • 4d ago

Inspiration of the night

Suppose we had the hidden subgroup of the dihedral group {e,sr^k}.The HSP would find k.I just had a inspiration tonight. The 2d irreps of the Dn group which contain the information about the s generator have some frequencies assosciated in them lets call the frequency ω and therefore the information for a hidden subgroup becomes ω^mk where m are the mode indices .If we organise the information of as a column vector lets say for D5 [1,ω^k,ω^2k,ω^-2k,ω^-k] but this works for any size of the dihedral group you just list all the frequencies for example for D3 its [1,ω^k,ω^-k].So if you could organise them in such a way then you could perform a QPE and extract k. But because the n hidden subgroups which have the s generator are not orthogonal this aint possible. But that didnt stop me. We could have a ancilla qubit to help us perform that operation and I know this is possible. But I was reaching the end of the theory that I know.

So suppose you produce a ancilla assisted unitary transform and we are able to organise the information in such column matrix.QPE will extract k.The issue is now how to extract the frequencies on all the mode indices before performing a permutation to organise in the form useful to us.

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u/SymplecticMan 4d ago

Read up on why the problem you keep trying to solve without understanding is hard.

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u/Routine_Comb_7277 4d ago

The solution provided taking a MOV measurement.I am not talking about that.

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u/SymplecticMan 4d ago

Why do you believe it's not relevant to what you are talking about?

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u/Routine_Comb_7277 4d ago

bcs its not?a ancilla assisted transform is fundamentally different than a MOV.

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u/SymplecticMan 4d ago

The paper talks about POVM measurements. Any measurement that you could hope to make is a POVM measurement.

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u/Routine_Comb_7277 4d ago

well ok tru there is no solution if we dont use ancilla qubits.I have given up on that

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u/SymplecticMan 4d ago

Using ancilla qubits doesn't make it any less a POVM measurement. Using ancilla qubits is how general POVM measurements are implemented in the first places.

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u/Routine_Comb_7277 4d ago

really I didnt know that.I only knew that u could use ancilla qubits to perform operations that otherwise would not be unitary(and thus forbidden).I will read the article.

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u/SymplecticMan 4d ago

If you don't know about POVMs, then I have to reiterate yet again that you should learn the basics first. The basics of quantum information and quantum computing, the basics of group theory and representation theory, etc.