Salman Beigi

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Quantum computing (in Farsi)

• Lecture 1: Review of the subject
• Lecture 2: Review of linear algebra, Dirac’s notation
• Lecture 3: Postulates of quantum mechanics 1
• Lecture 4: Postulates of quantum mechanics 2
• Lecture 5: Density matrices, partial trace
• Lecture 6: Purification, EPR paradox
• Lecture 7: Quantum circuits
• Lecture 8: Quantum gates, Deutsch-Jozsa algorithm
• Lecture 9: Grover’s algorithm, Shor’s algorithm
• Lecture 10: Quantum CPTP maps
• Lecture 11: Trace distance, fidelity
• Lecture 12: Quantum error correcting codes 1
• Lecture 13: Quantum error correcting codes 2
• Lecture 14: Quantum error correcting codes 3

Quantum information theory (in Farsi)
prepared jointly with Amin Gohari

Linear Algebra

• Lecture 2: Vector space, Dirac’s notation, inner product, change of basis
• Lecture 3: Elementary row/column operations, rank, eigenvalues and eigenvectors
• Lecture 4: Linear operators
• Lecture 5: Matrix representation, functions of operators, adjoint, Schur decomposition
• Lecture 6: Unitary, hermitian, normal, singular value decomposition
• Lecture 7: Direct sum and tensor product of vector spaces: motivation and definition
• Lecture 8: Linear operators on tensor spaces, Schmidt decomposition

Postulates of Quantum Mechanics

• Lecture 9: Postulates of quantum mechanics: state space and measurement
• Lecture 10: Postulates of quantum mechanics, Heisenberg’s uncertainty principle
• Lecture 11: Superdense coding, teleportation, EPR’s hidden variable model
• Lecture 12: Density matrices, ensembles
• Lecture 13: Coding in a quantum state
• Lecture14: Partial trace 1
• Lecture 15: Partial trace 2
• Lecture 16: Purification
• Lecture 17: Quantum CPTP maps 1
• Lecture 18: Quantum CPTP maps 2
• Lecture 19: Trace distance and fidelity

Quantum Information Theory

• Lecture 20: Classical concepts of typicality, KL-divergence, source coding and channel coding
• Lecture 21: Definition of a quantum source and channel, entropic expressions and inequalities
• Lecture 22: Tools from linear algebra, operator monotone and operator convex functions
• Lecture 23: Properties of von Neumann entropy
• Lecture 24: Entropy of measurement, majorization
• Lecture 25: Quantum typicality, Schumacher compression and Fannes-Audenaert inequality
• Lecture 26: Schumacher compression, quantum channel coding (Holevo information)
• Lecture 27: Holevo information 2
• Lecture 28: Entanglement distillation, entanglement of formation, LOCC maps