ABOUT THE COURSE:This course is based on the course Quantum Information Processing that I have been giving at IISER Kolkata for more than 6 years, the link of the course is: ://www.iiserkol.ac.in/teaching-plan/course/2022/Spring/PH4207/This course is meant for 4th year B Tech or BS students who have the prerequisites of Intermediate Quantum Mechanics, Mathematical Methods and Statistical Mechanics. Here the course is somewhat formal and not very application oriented. Some background in linear algebra is desirable. We assume the students to be familiar with Hilbert Space structure and inner product and the bra ket notation. However, rotation operators etc will be introduced in the course for quantum gates. Some knowledge of Tensors would be helpful, however, if the student does not know, then it would be introduced.INTENDED AUDIENCE: Masters or advanced undergraduate studentsPREREQUISITES: Basic Quantum Mechanics, Basic Statistical Mechanics, Basic Mathematical Physics, Condensed Matter Physics, Basic OpticsINDUSTRY SUPPORT:Cybersecurity & Cryptography: The course covers classical and quantum cryptography, including RSA encryption, which is fundamental to securing data and communications. Finance & Data Science: Topics like Shor's algorithm for factorization and Grover's search algorithm are highly relevant for a future in finance and data analysis, as they offer the potential for faster data processing and complex problem-solving. Technology & Computing: The course delves into the physical realization of quantum computers, including NMR and superconducting qubits. This is crucial for hardware development in the computer industry. Telecommunications: The study of quantum protocols, such as teleportation and quantum dense coding, is directly applicable to developing new methods for secure and efficient communication. Aerospace & Defense: The principles of quantum computation and information theory have potential applications in advanced navigation, satellite communication, and secure systems for the aerospace and defense sectors.

Syllabus

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.
Week 2:Single qubit operations and measurementsState space of two qubits; Multi-component systems and Product basis; Tensor products; multi-qubit operations. Deutsch’s algorithm, power of parallelism in quantum mechanics
Week 3:Information is Physical, Bloch Sphere, Rotations on Bloch Sphere Pauli Gates, SU (2) symmetry, quantum gates, Rotations in terms of Euler decomposition.
Week 4:Density Matrix, Pure and Mixed States, Properties of Density Matrix,
Week 5:Information Theory,Classical information theory Information Functional, Classical information theorem, Shanon entropy, Quantum Information Theory, von Neumann entropy.
Week 6:Entanglement in pure states, reduced density matrix, partial tracing, Schmidt decomposition and singular value decomposition; Bell states
Week 7:Quantum Protocols, Experimental Teleportation and Quantum Dense Coding: EPR Paradox and Bell’s inequality and CHSH inequality
Week 8:Classical and quantum cryptography, RSA encryption. Discrete Fourier Transform and Quantum Fourier Transformation
Week 9:Factorisation and Shor’s algorithm and Grover’s search algorithm
Week 10:Decoherence and open Quantum systems, Examples of Decoherence, Lindblad Master Equation: Example
Week 11:Entanglement in mixed states Entanglement in Mixed States, Convex Sum Theorem, Peres-Horodecki Criterion, concurrence
Week 12:Physical Realization of Quantum Computers, NMR and superconducting qubits