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Most of the information devices we use today, such as PCs and smartphones, web servers that send out information on websites, IoT devices, and mission-critical systems that control power supply, are processed by computers called Neumann-type computers.

The Ising model is the simplest model in a field of physics 'statistical mechanics'.

Those who have followed the path of science may not need an explanation as to why an annealing machine derives the optimal solution from the cost function, but for those who have not, it may not be quite so clear.

To solve optimization problems, events must be expressed numerically.

Let me explain how to formulate the equation in light of the case of the 'Image Noise Reduction' demo application on this site.

Not every optimization problem can be dramatically improved with an annealing machine.

A linear programming problem is one that can be represented by a linear function.

The aforementioned first-order equations can be easily solved by other methods, whereas the second-order optimization problem is considered to be efficiently solved by an annealing machine.

So when does this second-order term appear in a real problem?

One reason why combinatorial optimization problems are difficult is that they are discrete-valued.

Solving an optimization problem with an annealing machine means that the elements to be combined are represented by an Ising model.

We have described examples of problems that can be put into an annealing machine and solved efficiently, but when there is a problem around us and an opportunity to solve it using IT, we need to accurately identify the nature of the problem, select the right solver (software or solution for solving the problem), and then use it to solve the problem.

What is a typical combinatorial optimization problem? Many people may answer with the 'traveling salesman problem'.

Both machine learning, which is often used in AI, and annealing machines, which perform combinatorial optimization, are computers that perform difficult processing on behalf of humans.

An annealing machine is a technique for solving combinatorial optimization problems through a mechanism in which the ground state of the Ising model (the state with the lowest energy) gives the optimal solution by setting preconditions that result in the optimal solution.

In the second part, we will discuss the structural specifications and technical challenges of the annealing machine that actually derives the ground state of the Ising model.

When applying an annealing machine solution of an optimization problem to a real-world problem, the ultimate goal is to improve the user's work through the optimization process.

In this section, we will look back at the roles that hardware and software have played in the shift from the dawn of annealing machines to their widespread use, and also consider the roles they will play in the future.

This column introduces recommended books outside of Annealing Cloud Web that you should deepen your knowledge in order to actually use an annealing machine.

In general, computers often employ procedures and algorithms that lead to the only correct solution (exact solution), but let's learn about the different heuristic features and the significance of annealing machines in this perspective.

Did you know that annealing machines are already being used in business, not just for verification, but as a means to solve real-world problems? This article will cover examples of applications that have been published so far.

This column is filled with hints for advancing issue clarification and requirement definition, so if you're unsure where to start or how to articulate your thoughts as you progress in your study of mathematical optimization, please take a moment to read it.

In order to encourage more people to use an annealing machine, we have published an article explaining the process of solving optimization problems with annealing machines for beginners.

In this article, we explain how to organize information of the problem that you want to solve, which will be done in the requirements definition stage, using the 'school class timetable' as a motif.

Solving a combinatorial optimization problem with an annealing machine requires a process called Ising model formulation.

In this article, we will create input data for the number partitioning problem that we have made 'formulation' in the previous article.

Let's input the data for the number partitioning problem created in the 'Input Data Preparation' section into the CMOS annealing machine to solve it.

This tutorial explains the processing of the annealing machine in the demonstration application 'Ising editor'

This tutorial explains the processing of the annealing machine in the demonstration application 'Image noise reduction'.

This tutorial explains the processing of the annealing machine in the demonstration application 'Building network robustness'

The Annealing Cloud Web API provides Web API for performing operation of an annealing machine using Ising model via HTTP.

Annealing Cloud Web API provides annealing machine operations using the Ising model as a Web API that communicates via HTTP.

In Ising editor, you can set parameters and schedule of CMOS annealing machine and perform annealing.

The Ising editor is a learning tool that provides a visual representation of the CMOS annealing machine in action, but it is a unique tool for visually seeing what to input to the CMOS annealing machine and how to obtain a solution.

This demo app is to solve the problem of estimating the original image from a noisy black and white image with an annealing machine.

This demo app is to solve combinatorial optimization problems with an annealing machine taking as an example a problem called vertex cover problem of graph.

This article provides an exercise to realize a signal control system to relieve traffic congestion as a signal control system by processing it with a CMOS annealing machine as a combinatorial optimization problem.

With the Fitness diagnostic tool, you can confirm whether the optimization examples or problems you are familiar with are actually compatible with an annealing machine.