Quantum Information Science I, Part 3

• Overview of classical error correcting codes - intro
• Hamming's classical error correction code and linear codes
• Classical linear code minimum Hamming weight
• Classical linear error correction code distances
• The parity check matrix H
• Classical linear code error syndromes
• Determining the error from the syndrome for classical linear codes
• General Hamming classical error correction codes
• Classical linear codes - dual and self-dual codes
• What is a noisy quantum state? Introduction to density matrices
• Indistinguishability of density matrix ensemble unravelings
• Measurements and density matrices
• Action of unitary transform on density matrices
• Effect of measurement on an ensemble of states
• Density matrix properties
• The role of density matrices in the phase estimation algorithm
• Density matrices and the partial trace - example
• Density matrices and the partial trace - definition
• Equivalence of density matrices to partial trace computed in different bases
• Bloch sphere representation of single qubit density matrix states
• Quantum channels - simplified: the dephasing channel
• The dephasing channel as depicted on the Bloch sphere
• The depolarizing channel
• Quantum version of the classical repetition code - three qubit bit flip code
• The three-qubit phase flip error correction code