Several questions about QUBO problem resolution

[trainenjoyer]

I have several questions about Quandela’s way of solving a QUBO problem:

• First of all, is your implementation here : The shortest path problem using QUBO — perceval 0.10.2 documentation (1) work for every problem expressed in QUBO ?
  I feel yes, but how to chose the initial parameters ? I don’t see how to link the initial parameters to the problem we want to solve : do we have to choose the parameters so the initial distribution is near the solution ? This would imply having an idea of the initial distribution

• Secondly, why don’t you adapt the method described here Variational Quantum Eigensolver — perceval 0.10.2 documentation for solving the shortest path problem ?

-Finally, still considering this : (1) I don’t understand how to choose the optimal configuration : in this specific case, we can see why the others don’t match : but in general, I don’t know how we could distinguish the other configurations, especially if the system return two different states in high majority in two different configurations.

Thank you in advance

[anafilipacarv98]

Hello,

The algorithm is meant to work on every problem expressed as QUBO, given the matrix describing it. For the initial parameters, the values from the original paper (https://arxiv.org/pdf/2112.09766.pdf) are random values. You could see the same in VQE algorithms. You can have some freedom though and, for the hackathon challenge 2022, the participants decided to use that over a random initial vector.

The goal of the challenge was to use and explore QUBO to solve the shortest path. Indeed, you can apply VQE also or any other suitable algorithm to solve the use case.

Finally, for the different states that the algorithm returns, the original paper referenced before mentions the explanation for it. It is related to the output states that one can reach with the specific input tried and it leads to multiple states to compare.

[trainenjoyer]

Okay, thank you for your answer !