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In this tutorial https://qiskit.org/textbook/ch-paper-implementations/tsp.html I understood most of the steps of how to build it, but not the result. In the code, I see they don't get to the part of doing grover search. I think, they only get to this part of the approach they mention:

  • "Then we apply phase estimation algorithm to certain eigenstates which gives us all the total distances possible for all the routes".

I am not sure if I understand that sentence. As I understand, an eigenstate represents a path that goes through each city (encoded in binary with the function they show). I thought reading and running the code would make it clearer, but the output of the code when ran is '100100' for the eigenstate '11000110'. Is that supposed to be the total distance for the path that represents that eigenstate? '100100' is 36 in decimal, is that encode in some way? or is actually that the cost of that path?

-- edit: I know the distances are represented as phases, so they are bounded between 0 and 2*pi, but i don't get what that '100100' could be

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$100100$ is the string of $t$ bits of the estimated phase. You have to read it as $\varphi = 0.\varphi_1\varphi_2...\varphi_t$.

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  • $\begingroup$ Since you mentioned the estimated phase, I figured my problem was my ignorance about phase estimation algo, so i checked this qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html . So according of 2.2 results in that link, in this case I would need to do 100100=36 in decimal, and 36/(2^6)=36/64, so that's the estimated phase? ( I dont get φ=0.φ1φ2...φt this). $\endgroup$
    – Sfp
    Jan 25 at 0:58
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    $\begingroup$ 0.100100 means $0 \cdot 2^0 + 1 \cdot 2^{-1} + 0 \cdot 2^{-2} + 0 \cdot 2^{-3} + .. = 0.5625$, which is your estimated phase $\endgroup$
    – Michele Amoretti
    Jan 25 at 8:35
  • $\begingroup$ in the table of 'circuit' section we can see the distances for the hammiltonian cycle 1-2-3-4-1, are 𝜋/2+𝜋/4+𝜋/8+𝜋/4=(9/8)𝜋 , 9/8=1.125. We know 0.5625 is the eigenvalue which is the total cost, but how is 0.5625 related to 1.125? $\endgroup$
    – Sfp
    Jan 25 at 17:00

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