Quantum Error Correction: Andrew Landahl David Gottesman Dr. Wu And others

Stabilizer measurement?? l This is implementing a measurement (interpreting 0 as +1, and 1 as –1) Z1Z1

l This is implementing a measurement Stabilizer measurement?? Z1Z1 Z2Z2

l This is implementing a measurement Stabilizer measurement??

Notation clarification l For an n-qubit system denotes l E.g. n=3, then What does it mean Z 1 Z 2 ?

The Shor Code as a Stabilizer code

Stabilizer codes

Stabilizer Codes by Gottesman, 1997

Classical (7,4,3) Hamming Code C 1

Stabilizer for Steane code

Steane code: based on Hamming code

Vector Space under Symplectic Inner Products

Weight and Distance

Theorem for Existence of Additive QECC

Stabilizer for 5-qubit [5,1,3] code

Symplectic Form for Stabilizer

Commuting Group

Linear Block Codes

Standard Symplectic Form

Encoder for Stabilizer Codes

[5,1,3] Quantum Encoder (X part) (5,1,3) code

Complete [5,1,3] Quantum Encoder (5,1,3) code