Quantum Error Correction

Contents

Basics of Quantum Information: quantum states and density operators; reduction of quantum states via partial trace; projective measurements; characterization of quantum channels; the Kraus representation of quantum channels.
Quantum Noise and Error Correction: Examples of single and multi-qubit quantum channels and errors; Examples of quantum error correction: the Steane code, the 3-qubit code and the Shor code.
Stabilizer Codes: The Pauli group; definition and properties of stabilizer codes; ; quantum error correction conditions for stabilizer codes; discretization of errors; distance and size of stabilizer codes; sets of detectable and correctable error patterns, minimum distance; symplectic representation of Paulis; CSS codes.
Other Topics: introduction to surface codes and quantum LPDC codes, fault-tolerant quantum computation.

References

Books
- Daniel Gottesman, Surviving as a Quantum Computer in a Classical World
- Michael A. Nielsen and Isaac L. Chuang, Quantum Information and Quantum Computation
- John Watrous, The Theory of Quantum Information
- Phillip Kaye, Raymond Laflamme and Michele Mosca, An Introduction to Quantum Computing
Video Lectures
- Prabha Mandayam, Quantum Error Correction and Quantum Information Theory
- John Watrous, Understanding Quantum Information and Computation
- Artur Ekert, Introduction to Quantum Information Science