Summary
This chapter has been devoted to introducing two different mathematical frameworks, the Ising model and the QUBO formalism, which allow us to write combinatorial optimization problems in a way that we will later be able to use to find approximate solutions with the help of quantum computers. We started with some simple examples and worked our way up to some famous problems such as graph coloring and the Traveling Salesperson Problem.
In order to achieve that, we studied different techniques that find wider applications in the process of writing optimization problems for quantum computers. We saw, for example, how to use slack variables and how to replace constraints with penalty terms. We also learned how to transform integer variables into a series of binary ones.
After all that we have covered in this chapter, you are now prepared to write your own problems in the languages required by optimization algorithms that can run on quantum computers. The rest of the chapters in this part of the book will be devoted to learning how to implement and run those quantum optimization algorithms. In fact, in the next chapter, we will explain how to use a type of quantum computer called a quantum annealer to solve QUBO and Ising problems.
