Quantum Information Science II, Part 1

A trivial quantum stabilizer code

Action of unitary transform on density matrices

Alternate formula for the projector into the stabilizer subspace

Any stabilizer code can be mapped to the trivial code: towards the Clifford group

Axiomatic definition of quantum operations

Equivalence of forms of quantum operations

Bloch sphere representation of single qubit density matrix states

Equivalence of symplectic transformations to Clifford operations

Classical error correction codes – a review

Equivalent version of the quantum error correction conditions

Classical linear error correction codes – definition

Error correction code distances and error detection

Classical linear error correction codes – field F2

Error rate reduction by combining codes to get Shor 9-qubit code

Classical random maps

Example – n-bit repetition code

Code distances and error correction

Examples of quantum operations

Composition of quantum operations

F2 perspective on stabilizers – binary symplectic form

Concatenated quantum error correction codes

Introduction to quantum information science

F2 picture of Clifford operations – analogy to Lorentz group

Density matrices

F2 picture of Clifford operations – application to the trivial code