Quantum Information Science II, Part 1

Introduction to quantum operations

Density matrices and ensembles

Introduction to stabilizer codes

F2 picture of Clifford operations – conjugation formula

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