# traveling salesman output from qiskit docs

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

$$100100$$ is the string of $$t$$ bits of the estimated phase. You have to read it as $$\varphi = 0.\varphi_1\varphi_2...\varphi_t$$.
• 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 Jan 25 at 8:35