Not every optimization problem can be dramatically improved with an annealing machine. Annealing machines are a technology that is being researched and developed with the hope that they can efficiently solve problems that meet certain conditions and are difficult for conventional computers to solve. Although efficient methods exist for solving many optimization problems, there are theoretically some very time-consuming and unsolvable problems. However, the first step in mastering the annealing machine is to know which optimization problems can be solved efficiently or not so efficiently. Once you have learned and understood how to classify optimization problems, the way to think about solving them with an annealing machine, and how effective they are, the next step is to deepen your knowledge of what kind of problems can be dramatically improved.

There have been many difficult optimization problems and their solutions (algorithms)have been studied in various ways. The theory of the Ising model incorporated into the annealing machine was created to solve "very difficult" problems that could not be solved very well. To understand the nature of such problems, let's start with an example of a typical problem that can be solved without an annealing machine.