MIT

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

The five-qubit code – stabilizers

Gottesman-Knill theorem – statement

QEC example 2: classical code in the Hadamard basis

The five-qubit code is a non-degenerate code