# How would D-Wave be used for complex optimization problems? [closed]

We are interested in solving an optimization problem, and specifically, the design of efficient yacht hulls.

In designing an efficient yacht hull, one must consider water-hull resistance, wave generation, near-field and far-field wake, side pressure, velocity prediction, and stability. The design is typically done with simple computational fluid dynamics. Sail design complicated the problem.

Thus, there are hundreds of equations to optimize to find a good yacht.

Is this a question which today's DWave can develop answers?

I read DWave gives too many answers for equation systems. My boat designs will be optimized for one speed and free curves and they will be very beautiful.

I want to get a good computation in short time.

What do you think, what would be the time taken to do this using a DWave machine?

• Welcome to Quantum Computing SE! Would you be able to write (at least some of) the equations down here? Or link to them? Optimising yacht designs sounds unusual compared with most other applications but that certainly doesn't mean the answer is 'no', if we could have some more mathematical details about what's being optimised Aug 3 '18 at 11:21

So I do not know much about yacht design but having played a little bit with a D-Wave machine I would suggest to see if you can model your problem as a Quadratic unconstrained binary optimization. See on Wikipedia.

That is your variables must be binary and a D-Wave machine will try to find a minimum to your QUBO. It will return many answers in a sense that it tries multiple times to find it but the goal is to find one minimum or sample near it with this minimization objective. If you ask for 1000 tries, it may give you a 100 different solutions but some with more frequencies.

Now about the time to do it, it will depend on how the problem can fit in the hardware. You have to take into account the number of variables and their connectivity (which variables share a coefficient in the QUBO) and finally see if it fits with the number of qubits and their connectivity on D-Wave.

Say you can fit it, it will give you answers quickly. Depending on numbers of runs you ask and time parameters for each run you pass, it will be a matter of seconds.

For example of a QUBO, here is a the simplest one : $$x_0 + x_1 -2x_1x_0$$, where

$$x_1$$ and $$x_0$$ are my binary variables (0 or 1 values). Here two solutions: (0,0) and (1,1).

To solve this on the machine, you generally pass a file/dictionary/table that looks like this and represent your QUBO problem:

0 0 1 (coefficient of x0 with itself)
1 1 1 (coefficient of x1 with itself)
0 1 -2 (coefficient between x0 and x1)