Quadratic Unconstrained Binary Optimization (QUBO) problems

We will now focus on understanding what kind of problems are solved by a quantum annealer and how a problem is mapped onto the annealer. This process is the same for any solver that can solve QUBO problems. These are a special class of problems where you have binary variables and the relationship between them is no more than quadratic. In other words, you can have the product of two variables but not three variables, and you can have the square of the variables but not the cube or higher. In addition, the variables can only have the values of 0 or 1 (binary) or +1 or -1 (spin).

You can see the following equation as a representation of a QUBO problem. When solving this type of problem, we are trying to minimize the cost function shown in equation 5.1.

This equation can be written in many forms; however, I will use this format so that I can distinguish between the linear terms on the left and the...