Developing Quantum Expressions using QUBO

[rpthomps]

TL;DR Summary

I want to build an expression to solve the two ways to sum to the value of 8 using a set of five numbers 1 , 2, 3, 4, 5 and the criteria is only three numbers can be chosen.

Hi there, I would like some help developing a QUBO expression where a Quantum Annealing approach would find the two ways of summing the 5 numbers {1 2 3 4 5) to 8 by selecting 3 of the numbers. I am basing this off of a dwave.sys video example I found on their site.

My initial kick at the can, looks likes this:

(x₁+2x₂+3x₃+4x₄+5x₅-8)²+(x₁+x₂+x₃-3)²

I saw a chart in a paper with penalties so I guess, I would also subtract (x₁x₂+x₂x₃+x₁x₃)

What I would like is another expression of a similar vein with the solution so I could analyze it an understand what is happening. Any thoughts/help would be appreciated.

 

[azntoon]

Here is a QUBO expression that will find the two ways of summing the 5 numbers {1, 2, 3, 4, 5) to 8 by selecting 3 of the numbers: QUBO: minimize (x1 + 2x2 + 3x3 + 4x4 + 5x5 - 8)^2 + (x1 + x2 + x3 - 3)^2 + (x1x2 + x2x3 + x1x3)where x1, x2, x3, x4, x5 are binary variables (0 or 1). The first two terms in the QUBO expression are the objective function. The third term is the penalty term, which penalizes any solutions that have more than three variables set to 1. The solution to this QUBO expression is x1 = 1, x2 = 1, x3 = 1, x4 = 0, x5 = 0. This corresponds to {1,2,3} as the three numbers that sum to 8.