### Join the D-Wave Leap Quantum Coding Challenge: Problem 1

Back in October 2018, D-Wave launched a cloud service to provide everyone access to their 2000+ qubit quantum computer. Now, they are releasing the D-Wave Leap quantum coding challenge to encourage people to use their cloud service and teach.

Though no math or physics degree is required, there are some terms and concepts that would be helpful for you to complete the challenge and fully understand why these are interesting problems to tackle. This will help build up your understanding of quantum computing.

Sign up for Leap here, and let’s get started! Remember, you can get a free minute every month with their developer plan. Just enter your Github username and repository for your D-Wave and open source your work.

## D-Wave Leap Quantum Coding Challenge: Problem 1

The first problem of the D-Wave Leap Quantum Coding Challenge is to maximize the classical gap of a two-qubit system. In short, we need to have the difference in energy be as large as possible.

So why do we care about all of this?

The D-Wave quantum computer is a quantum annealer (read about the differences between an annealer and universal quantum computer here.) Quantum annealers are very good at optimization problems. The Ising model problem is one of these where D-Wave and annealers can offer a speedup over classical solvers. Also, optimizing the energy gap to be large determines the efficiency of the quantum annealing. The more efficient the annealing, the likelier we can get a correct and fast response from the annealer.

The equation that we need to solve is:

where s is the spin variable, J is the coupling constant, and E is the energy.

Let’s dive deeper into each variable and the terms of the problem, and what they mean.

### Spin variables

In atoms, the nucleus spins – meaning, it has angular momentum. Spins that are positive are spin “up” and spins that are negative are spin “down”. This problem tells us the spin variables are either +1 or -1, and that the spins are not equal to each other.

So,

since one of the spins has to be +1, and the other is -1.

### The coupling constant J

J is called the coupling constant, or the interaction strength of the two spins. In this problem, we are looking for the value of J, the coupling constant. The coupling constant will be between -1 and 1, and we need to select the value that will make the energy less than zero.

We can also turn this around, and examine how magnetism is related to the coupling constant if the two spins are the same or if they are different. If J is negative, nearest neighbors have the same spin. This is called ferromagnetism. However, if J is positive, nearest neighbors have opposite spins. This is called anti-ferromagnetism.

Here’s a quick video explanation on ferromagnetism:

### The Ising model

To describe magnetism, we use the Ising model. Our model here is very simple – just two spins and makes it simple to solve by hand. However, as the dimensions and complexity of the Ising model grows, and the solution of the Ising model is much harder to find.

Understanding the Ising model and spin is the first step in understanding quantum annealing and the types of problems the D-Wave computer can solve. Click here to try the challenge! Remember, you can sign up to use the D-Wave machine today and run algorithms to do factoring, social network analysis, and materials simulation.

*Are you going to try out the D-Wave quantum computing challenge? What do you think will be the next challenge? What concepts will help you understand more about what the D-Wave machine does?*