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Quantum Computing

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  • $\begingroup$ Thank you @DaftWullie The $\xi_i$ can be calculated recursively, for $i=1,2,....n$, so one can build in advance all the quantum circuits implementing the operators $U_{\xi_i} = 2\vert \xi_i \rangle\langle \xi_i \vert - I$ which are unitary , and run the algorithm (quite a lot of them for large n). I was trying to avoid all that by considering only one quantum circuit implementing U, but it' looks like it's not unitary. $\endgroup$ Commented May 7, 2020 at 15:33
  • $\begingroup$ But surely you can only precompute them if you know in advance what you’re searching for? (also, I guess it’s hard for a classical computer to perform that precomputation) $\endgroup$ Commented May 7, 2020 at 16:18
  • $\begingroup$ "........if you know in advance what you're searching for". Understood, I see the problem, thanks. $\endgroup$ Commented May 9, 2020 at 7:15
  • $\begingroup$ You assume that the program states are not orthogonal. That's the key. Please have a look at this: quantumcomputing.stackexchange.com/q/12071/10110 Feedback appreciated @DaftWullie $\endgroup$ Commented May 18, 2020 at 23:48
  • $\begingroup$ No, I’m just assuming that your program has to be able to act on non-orthogonal states, which it does if it’s a quantum computer. $\endgroup$ Commented May 19, 2020 at 5:31