Quantum Error Correction

1.1-Vector spaces

1.2- Bases, norms, inner products

1.3- Linear Operators

1.4-Eigenvalues and eigenvectors

1.5- Adjoint, Hermitian and Unitary operators

1.6- Operator functions

1.7- Pauli and generalized Pauli matrices

1.8- Postulates of quantum mechanics

2-Introduction to quantum computation and information

2.1-Single and multiple qubit operations

2.2-Universal quantum gates

2.3- Bit flip and phase shift channels

2.4- Depolarizing channel

2.6-Measure of distance of quantum states

2.7-Fidelity

3-Quantum error-correcting codes

3.1-The Shor code

3.2-The Steane code

3.3-Five quibit code

3.4-Quantum Hamming and Singleton bound

3.4-Stabilizer codes

3.5-Calderbank-Shor-Steane code construction

3.6-Hermitian construction

3.7-Ste

3.8-Additive codes

4-Quantum code construction

4.1-Bose-Chaudhuri-Hocquenghem codes

4.3-Reed-Muller codes

4.4-Quadratic residue codes

4.5-Constacyclic codes

4.6- Affine Invariant codes

4.7-Algebraic geometry codes

4.8-Synchronizable codes

5-Asymmetric quantum code construction

5.1- Bose-Chaudhuri-Hocquenghem codes

5.2- Reed-Solomon codes

5.3-Tensor product codes

5.4-Alternalt codes

5.5- Algebraic geometry codes

5.6-New codes from old

6-Quantum convolutional code construction

6.2-Quantum convolutional codes

6.3- Code construction: Bose-Chaudhuri-Hocquenghem,

Reed-Solomon

Reed-Muller