The decoding problem

Previously, we learned how to define a quantum error correcting code by making use of the stabilizer formalism. We also learned how one can use take non-destructive measurements of the code's stabilizers to obtain a syndrome. We encouraged you to use the simulation package plaquette to input many stances of errors and learn what kind of syndrome should you expect given an error. A syndrome, as we also saw, is degenerate, which means that many different errors can give the same syndromes.

Errors with the same shape as stabilizers and logical operators do not toggle any of the stabilizer measurements. In the case of the former, the error is trivial because applying a stabilizer to the state leaves it unchanged. The latter is not trivial and posses a serious issue: a logical operator has been applied to the code, and we'll never be able to detect it! All of our future calculations with that logical qubit will return wrong results.

Therefore, we need a way to correct these errors when they occur, so they don't pile up and lead to a logical error. Let's find out how!

This module was developed in collaboration with QC Design.

About this module

In this module you will learn ...

• ... about decoders - algorithms that analyze error syndromes, determine the most likely error configuration, and ultimately correct those errors to recover the quantum information.

This module ...

• ... requires an understanding of quantum circuits and mathematical notations.

• ... requires you to have finished the Identifying errors in quantum computing module.

• ... requires you to get active and experiment with the tools provided.

• ... is better taken with friends or co-workers to actively discuss and speak about what you’ve learned.

Our modules are exploratory in nature. Thus, you will actively experience the different ideas of quantum computing, its algorithms and its applications.