Thursday 19 May 2016

Quantum Error Correction: The Puzzle

Tutorial in 5 seconds!
  • Do a Z10 easy game.
  • Numbers appear in small groups.
  • Each adds up a multiple of 10.
  • Guess the groups.
  • Work out what numbers are in the ? squares.

Extended tutorial for the
10 Puzzles (
auch auf Deutsch verfügbar.)  
The puzzles are based on a grid with numbers in small groups. We need to get rid of the numbers. The best way is to push all numbers from the same group together. But how do we find the groups? For this we can use two facts: every group adds up to a multiple of 10 and the groups are normally small.

Here's an example.

Here it's easy to find the groups. There is an 8 and a 2 together. They are neighbours and add up to 10. So probably this pair is its own group. The 6 and 4 are also neighbours that add up to 10. The 9 and 1 aren't neighbours, but they are close to each other. Presumably they form a group too, and so on.

Here the groups are all shown in different colours.

Sometimes we'll make a mistake in finding these groups. Small errors aren't a problem, but how big is too big? How can we find out whether our method is good enough?

Here is the same number as before, but without two of the numbers. Instead of the top-left and bottom-right numbers, we have question marks.

What is the top-left number, hiding behind the question mark? Of course we already know that it's an 8. But it is still obvious even without that knowledge. The other numbers already have their own groups. Only the 2 is alone. It needs an 8 nearby, so the top-left must provide it. No numbers need the bottom-left, so it must be empty. 

To help you keep track of the groups, you can colour them yourself. Simply click on them to cycle through a range of colours. And when the different colours run out, it'll go through them again but in italics, allowing you to distinguish between over 20 different groups.

The Φ-Λ Puzzles 

The Φ-Λ puzzles are pretty much the same as 10. The only difference is that you get less information about the numbers.

The squares hold either a Φ or a Λ, which are the Greek letters Phi and Lambda. If you have a Λ, you know that that the square holds a 5. If it is a Φ, you only know that it is something else: a 1, 2, 3, 4, 6, 7, 8, or 9. So the puzzle above would instead look like this

You can do science!

Our puzzles take place in a quantum computer, which are unfortunately pretty noisy things. They have far too many errors to solve even the simplest of problems. But we can help them. We can find clues about the errors that have happened and work out where they are and how to get rid of them.

It's a quantum puzzle, but it's not a complicated one. You don't need a PhD to solve it. Anyone can help. So you can find a good method and share it with us. And you could win a prize in our competition.

For more information on the science behind our puzzles, as well as their sister games, see here. You can also check out our main website.


This blog and the puzzle were developed by me, Dr James Wootton. I'm a scientist at the University of Basel, where I do research on quantum error correction. The project is supported by the NCCR QSIT, which supports research on quantum technologies in Switzerland. See here for more information on the Decodoku project.