Quantum Error Correction 6: [7,4] Hamming code, Linear codes, and [[7,1,3]] Steane code

In this video, I talk about the [7,4] Hamming code introducing the idea of parity check bits and how they help in the correction of bit flip in the case of classical codes. Following this I discuss the generator matrix and parity check matrix for linear codes. I introduce these concepts using the example of the Hamming code. Finally, I talk about the Steane code which uses 7 physical bits to encode 1 logical bit and can correct any single qubit errors. I discuss the stabilizers for the code highlighting how they form the faces of parts of a triangle. #quantuminformation #quantumcomputing #quantumphysics