Fault tolerance and quantum error correction

Fault Tolerance (FT) and Quantum Error Correction (QEC) are complex concepts and so it is worth asking: why study them at all?

This is an honest question, mostly because if you are approaching the field of quantum computing for the first time, getting your feet wet with cool concepts like QKD or quantum algorithms, most of the time the introductory material about these topics make a tiny assumption: you have perfect qubits. Not only that, you are actually dealing with perfect logical qubits.

If your curiosity was struck by press releases and articles in non-technical journals, these concepts might be foreign. We put emphasis on logical qubit, so what other qubits are there to talk about? We usually distinguish between logical and physical qubits. The latter are the ones we routinely make and manipulate in the lab, but they are too fragile to be used as reliably as we need them to. Physical qubits constantly and inevitably interact with their environment, and the gates we act on them can never be perfect. Together, this makes it hard to use and reason about them in a deterministic way.

That's fault tolerance in a paramount. You will never be able to completely remove this inherent fragility in the physical qubits you are given, so you need to tolerate their problems, and fault tolerance is about coming up with clever ways to blend multiple physical qubits together in such a way that when used to make a single logical qubit you can be fairly confident that it will behave as you've been told in textbooks.

This module was developed in collaboration with QC Design.

About this module

In this module you will learn ...

• ... the basic concept of error correction codes and the stabilizer formalism, a critical tool used to develop and analyze quantum error correction codes.

• ... about different surface codes.

This module ...

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

• ... 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.