Quantum Information Science II, Part 1

Six stabilizer group examples

Measurements and dual norms

F2 picture of Clifford operations – using the symplectic inner product

Effect of single qubit rotation errors on the quantum code

Space of low-weight quantum errors

Efficient decoding of quantum codes

F2 representation of stabilizers – error detection and logical operators

Measurements as quantum operations

Special cases of density matrices – probability distributions

Eigenvalues of density matrices specify a probability distribution

F2 representation of stabilizers – linear algebraic properties

Norms and distance metrics for quantum states

Special cases of density matrices – pure states

Equivalence of density matrices to partial trace computed in different bases

Fundamental building blocks for quantum error correction codes: encoding, decoding, recovery

Operator measurement

Special cases of density matrices – qubits

General classical error correction codes

Overview – Three representations of quantum operations

Stabilizer codes and criteria

Generalized measurements – example: non-demolition measurements

QEC example 1 corrects more than just discrete bit flip errors

Gottesman-Knill theorem – proof

Stabilizer groups and the Pauli group

QEC example 1: classical codes