This lesson introduces the stabilizer formalism, which is a mathematical tool through which a broad class of quantum error correcting codes, known as stabilizer codes, can be specified and analyzed. This includes the 9-qubit Shor code along with many other examples, including codes likely to be better suited to real-world quantum devices. The lesson also discusses basic properties of stabilizer codes and how the fundamental tasks of encoding, detecting errors, and correcting those errors can be performed.
0:00 – Introduction
1:28 – Overview
2:08 – Pauli operations
5:15 – Pauli operations as generators
7:46 – Pauli observables
12:36 – Repetition code revisited
15:23 – Bit-flip detection
19:39 – Syndromes
22:49 – Stabilizer codes
26:26 – Examples
30:50 – Code space dimension
35:26 – Clifford operations and encodings
39:55 – Detecting errors
43:34 – 7-qubit Steane code
45:55 – Correcting errors
52:06 – Conclusion
Find the written content for this lesson on IBM Quantum Learning: https://learning.quantum.ibm.com/course/foundations-of-quantum-error-correction/the-stabilizer-formalism