## Friday, 29 January 2016

### What shape is the Earth? Find out and let me know!

There’s been a bit of a commotion recently about the shape of the Earth. Some found it funny, but I found it inspirational.

We live in pretty exciting times. We can work out for ourselves exactly what shape the Earth is. We don’t need to rely on scientists: we can be scientists.

To understand the basic principle we can use, let’s consider a situation that’s a bit less planet sized. Suppose you are in a city and you see something interesting. Maybe a car. A unique, one of a kind car: Chitty Chiity Bang Bang.

You obviously phone your best friend to share the excitement. How could you not? He tells you that he can also see Chitty Chiity Bang Bang. So now, thanks to the miracle of telecommunications, you suddenly know something about the position of your friend. You know he must be quite close, because you can both see the same car.

You tell him that Chitty Chiity Bang Bang is about 100 metres away from you. He says that it’s about 50 metres from him. So know you know that he can be no further than 150 metres away. But in what direction?

You tell him that you are standing directly in from of the car. If he says that he is behind, you know that he’s 150 metres right in front of you. If he says that he is to the side of the car, with it pointing towards his right, you know that he is over to your left. With a bit of pythagorus you can work out the distance. With some trigonometry you can work out what angle.

So just because you can talk to each other, and because you can see the same object, each can work out exacty where the other one is. That’s something we’d probably think of as quite obvious. But it’s nevertheless pretty awesome.

What’s this got to do with the shape of the Earth? Well, we can apply the exact same principle. First we need a bunch of friends all over the world. Then we need some object that we can all see. Fortunately, we have a couple to choose from: the Sun and the Moon. The stars could come in handy to.

Get on Skype with your mates to make sure you are all looking at the same thing at the same time. Compare notes on where the Sun is. Don't look at it of course.
It won't do your eyes any favours, and it's not easy to get good measurements like that either. You're better of working out where it is using shadows. Is it directly overhead for some of you, near the horizon for some and not visible for others? What would that imply about the shape of the Earth? You can do the same thing for the Moon, but you can get a bit fancier. If it’s a half moon, what is the angle between the halfway line and the horizon? How does that change for your friends. You could compare the position of Orion’s belt in the sky and its angle to the horizon too. There’s loads of measurements you could make!

Then you can start thinking about what your reslults mean. You can try to work out what shape the Earth would need to be for you to get these results. If you get a bit of maths out, you could even try to work out how big the Earth is, and how far away the Sun is. All using the same techniques as when you worked out where your friend was using Chitty Chitty Bang Bang.

Once you’ve thought about it long enough. You will finally know what shape the Earth is. Not because someone told you. Not because you looked it up. With your own eyes and your own brain you figured out the shape of the Earth. You won’t need to trust anyone’s word on it. You will know it, more deeply and intimately than pretty much everyone else, because you worked it out for yourself.

Let me know what you find out.

This post is not the usual fare for this blog. I am usually talking about quantum error correction, which is more fun than it sounds. The first blog in the series is here

## Tuesday, 26 January 2016

### 2 - Storing Quantum Information

This is part of a project to get people involved with quantum error correction. See here for more info.

Storing Information

Last time we used error correction to help us send a message without getting messed up by errors. Here we will consider saving a message, for which we can also use error correction.

Suppose we have an important meeting, and need to remember the details of the appointment. Naturally we can write it down, but the paper can get lost or dirty. Is the information secure enough? If not, we can use error correction.

Let's use the repetition code, just like last time. We take multiple pieces of paper and write the time of the meeting on each. They are all then put in a safe place.

On the day of our meeting we gather up the pieces of paper. Maybe a couple have gotten lost, and some are too dirty to read. But the majority are probably fine. So we can get the information back using the same decoding as last time.

What if the meeting is in a year? More time means more errors. More of the pieces of paper will get lost, dirty or otherwise messed up. If it happens to too many, we won't be able to get the information back. What can we do?

We can expect that there won't be too many errors in just a week. So every week we can collect the pieces of paper, see what the majority is saying and replace everything else. Then no error will survive for long. The information will stay secure for a year or even more.

Quantum Information

Our current information technology* uses normal kinds of information like numbers, letters and pictures. The information technology of the future will use a new kind of information alongside this: quantum information. This follows the unusual rules of quantum mechanics. With quantum information, new methods for computation, communication and cryptography will become possible.

The magic of quantum information needs quantum superpositions. Normal information, for example, is either '0' or '1'. When it is 0 it is not 1, and vice-versa. We call this a bit. With quantum mechanics it can be 0 and 1 at the same time, and the two can influence each other. This is a quantum superposition. It continues until we measure it. Then it must decide which to be. We call such a quantum bit, a qubit.

A qubit is more complicated than a bit. They allow more complicated information technology. But they are fragile. So how can be protect our quantum information? With quantum error correction!

The problem of quantum error correction

As we've seen, storing normal information means looking at it often enough to catch the errors as they happen. With quantum information, that is not a good idea. As soon as we look at our qubits, the quantum superposition is gone. So instead of making things better, we've made them worse. We need to be careful to only measure exactly what is needed to catch the errors, and nothing more. But how to do this? We'll find that out soon. But next we'll look at exactly what this quantum stuff is all about.

* That's what IT stands for, by the way. It's not 'Internet Things'.

## Wednesday, 20 January 2016

### 1 - What is Error Correction?

This is part of a project to get people involved with quantum error correction. See here for more info.

What is Quantum Error Correction

What is quantum error correction. Is it as complicated as it sounds? First we will just look at error correction. Then we'll mix the quantum in later.

Suppose we want to send a message. We can never do this perfectly. It is always possible that it will get lost, damaged or garbled. When the probability of this is too high, we need to protect the message somehow. For this we use error correction.

Let's consider an example: you are talking on the phone with your friend. He asks you whether you'd like to come round for dinner, and you say 'Yes'. But the connection is bad: with a probability of 1 in 100 your answer gets garbled so much that your 'Yes' sounds like 'No'.

When you go to his house later, there will be no dinner. He heard 'No', and so wasn't expecting you. It will be a bit embarrassing, but it won't be so bad. A probability of 1% is not too high for the risk of a bit of embarrassment between friends.

If you have nuclear weapons, however, your conversations are much more important! Suppose you ask your boss whether it is time to launch the nukes. If he says 'No' and you hear 'Yes', it would be very bad. Naturally, we need to avoid this. A chance of 1 in 100 here would be much too high. The world is in danger!

How can we solve this problem? Your boss can change the message so that it is more robust. This method is call 'encoding'. A simple encoding is simply to repeat yourself.

Suppose that your boss doesn't just say 'No', but 'No! No! No! No! No!'. Maybe one of the words will get garbled and we'll hear something like 'No! No! No! Yes! No!'. There will still be many more 'No' than 'Yes', so you probably won't launch the nukes and the world is safe. If two get garbled there are still more 'No' than 'Yes'. So the message is still clear.

There will be more 'Yes' than 'No' only when three or more get garbled. In this case it seems like we should launch, which would be a big mistake!

What is the probability of such an error? We've already said that the probability of one word getting garbled is 1 in 100. The probability for three or more is then 1 in 100,000, which is a lot less likely!

If even this is still too high, we can repeat more than 5 times. If we used 7 repetitions, there needs to be four or more garbled words before we accidentally destroy the world. The probability of that is 1 in 3 million. The probability gets less and less when we use more repetitions.

In the above process we haven't just been using encoding. We have also used 'Decoding'. This is when we try to find out what message our boss has sent.

For the repetition encoding, this is very easy. We know that garbled messages are rare, so we trust the majority. When there are more 'No' than 'Yes', we assume that our boss said 'No'. For more 'Yes' than 'No' we assume 'Yes'.

In this example the message is easy to understand, even after encoding. That will not always be so. For more complicated encoding it can seem like nonsense if we don't recognize the encoding. The sender must therefore first explain the encoding method used. The receiver can then develop a decoding method. This will let them extract the original message from what they have received, even when it has gotten a little garbled.

Now we have all the ingredients of error correction. We have a message to send, and it is very important. So important that no error can be tolerated. To ensure that it stays secure, the sender uses an encoding method. The receiver then uses a decoding method to get the message out again, while correcting any parts that got messed up.

This is error correction in a nutshell, even when it's quantum.

## Wednesday, 13 January 2016

### Welcome to Decodoku

This is the blog for our project which aims to allow everyone to contribute to research on the exciting topic of quantum computers.

Here you will find information about quantum computers and quantum error correction. You'll also find out about our games, DecodokuDecodoku:Puzzles and Decodoku:Colorswhich let you take part in our research. The main series of articles can be started here. An overview of all our resources can be found here.

Decodoku and Decodoku:Colors have gameplay similarities to recent popular games such as Threes and 2048. Decodoku:Puzzles is a puzzle like Sudoku, or something else that you might find in a newspaper. But both are not just for fun, but for science!

All games are available on both iOS and Android as well as PC and Mac.

They are fun puzzle games to play while you wait for the bus. But, for those interested, they also give users everything they need to conduct their own research on how to keep quantum computers free of errors.

Once you've figured out a great method, you could keep it secret and sell it to Google. But you could also tell us about it and take part in our competition. Also check out our