Quantum Computation, Lecture 25, Stabilizer Error Correction, Mar 21, 2022
Channel: Deepak Vaid
Date: 2022-10-31

I introduce the stabilizer formalism for quantum error correction, using Shor's nine-qubit code as an example.

I explain why correcting a finite number of errors is sufficient to correct ALL continuous errors as a consequence of the linearity of quantum mechanics.

I introduce the Pauli group and explain the conditions that elements of the stabilizer sub-group must satisfy.

Edit: Oct 28, 2024

References for stabilizer codes (generated using Claude, please double check for possible errors)

arXiv:quant-ph/9705052
Gottesman's doctoral thesis, a canonical work introducing stabilizer formalism.

doi:10.1103/RevModPhys.87.307
Comprehensive review article on quantum error correction, including stabilizer codes.

doi:10.1103/PhysRevA.54.1862
Calderbank-Shor-Steane (CSS) codes paper, fundamental to stabilizer code theory.

arXiv:quant-ph/0602096
Pedagogical introduction to stabilizer codes by Daniel Gottesman.

doi:10.1103/PhysRevLett.77.793
Original paper on quantum error correction by Shor, laying groundwork for stabilizer codes.

arXiv:1907.11157
Recent review on fault-tolerant quantum computation, including stabilizer-based techniques.

doi:10.1088/1361-6633/aa8b28
Pedagogical review on quantum error correction and fault tolerance.

arXiv:quant-ph/0506023
Nielsen and Chuang's notes on stabilizer formalism, excellent for learning.

doi:10.1103/PhysRevA.52.R2493
Steane's paper on error-correcting codes in quantum theory, crucial for stabilizer development.

arXiv:1907.02554
Recent tutorial on quantum error correction, including stabilizer codes.