MIT

Density matrices and the partial trace – definition

Quantum states and operations – overview

Linear code example – repetition code

F2 picture of Clifford operations – decoding codes

Density matrices and the partial trace – example

Quantum version of the classical repetition code – three qubit bit flip code

F2 picture of Clifford operations – example

Linear codes: parity check matrices

Density matrix properties

Review: classical and quantum coding

F2 picture of Clifford operations – overview

Deterministic classical and quantum maps

Logical operators on quantum codes

Schatten p-norms

Mathematical definition of density matrices

Effect of depolarizing channel on the quantum code

F2 picture of Clifford operations – symplectic group

Schatten p-norms – review

F2 picture of Clifford operations – syndrome vector

Effect of measurement on an ensemble of states

Measurements and density matrices

Six stabilizer group examples

Measurements and dual norms

Effect of single qubit rotation errors on the quantum code

F2 picture of Clifford operations – using the symplectic inner product