Quantum Information Science II, Part 1

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

Stabilizer subspace

The key idea of quantum error correction – utilizing linearity

Quantum channels – simplified: the dephasing channel

Stabilizer subspace projectors I

Indistinguishability of density matrix ensemble unravelings

The multi-qubit Clifford group

Stabilizer subspace projectors II: size of the stabilizer group

Quantum codes – definition and review

The nine-qubit quantum error correction code

Quantum error correction criteria

Stabilizers

The physics of non-unitary dynamics in a unitary world

Quantum error correction in the Steinspring picture

Steinspring representation of quantum operations

The quantum error correction conditions

Syndrome measurement and recovery operators

Quantum mechanics and quantum circuits

The three-qubit phase flip error correction code

Syndrome operators – phase flip code and Shor 9-qubit code

Quantum operations as a composition of isometries and partial traces

Three conceptual challenges faced by quantum error correction