Week 1: Motivation and Introduction: Classical and quantum computers; Strong and Weak Turing hypothesis (Church-Turing version etc); Efficient and Inefficient algorithms; Advantages of quantum computation; Deutsch’s algorithm, power of parallelism in quantum mechanics.
Week 2: Single qubit operations and measurements State space of two qubits; Multi-component systems and Product basis; Tensor products; multi-qubit operations. Information is Physical, Bloch Sphere, Rotations on Bloch Sphere Pauli Gates, SU (2) symmetry, quantum gates, Density matrix.
Week 3: Density Matrix, Pure and Mixed States, Properties of Density Matrix, Euler decomposition, Information Theory, Classical information theory, Information Functional, Shannon entropy.
Week 4: Von Neumann entropy, Entanglement in pure states, reduced density matrix, partial tracing, Schmidt decomposition.
Week 5: Schmidt decomposition and singular value decomposition; Bell states, Quantum Protocols, EPR Paradox ; Bell’s inequality and CHSH inequality.
Week 6: Bell’s inequality, Quantum protocols: Quantum Dense coding and Quantum Teleportation, Generation of Entangled photons.
Week 7: Experimental Teleportation and Quantum Dense Coding, Prime Factorization, Classical and Quantum Cryptography, RSA encryption.
Week 8: Discrete Fourier Transform and Quantum Fourier Transformation
Week 9: Quantum Fourier Transform and quantum Circuits and Shor’s algorithm
Week 10: Decoherence and open Quantum systems, Kraus Operators
Week 11: Examples of Decoherence, Quantum channels, Lindblad Master Equation: Example
Week 12: Generalized Measurements, Positive Operator Valued Measurements, Entanglement in Mixed States, Convex Sum Theorem, Peres-Horodecki Criterion, concurrence
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