Syllabus

(8 hrs) Motivation for Quantum Technologies, classical vs. quantum computation, linear algebra (vector spaces, inner products, and norms), operators and matrices, eigenvalues and eigenvectors, tensor products, Dirac notation (bra-ket), quantum states, wave-functions, probabilistic interpretation, observables and measurements, projective measurements

(8 hrs) Quantum state evolution, quantum bits, quantum register, unitary evolution and quantum gates, basics of quantum correlations and superposition, two-qubit systems and Bell states, entanglement and its significance, controlled gates (CNOT, Toffoli, Fredkin).

(8 hrs) Quantum teleportation, no-cloning theorem, superdense coding, classical error-correcting codes, quantum error-correcting codes, Shor’s 3-qubit bit-flop code, error correction in quantum sustems.

(8 hrs) Overview and classification of algorithms, problem-solving on quantum computers, basics of Deutsch algorithm, Deutsch-Jozsa algorithm for decision problems, classical vs. quantum speed-up, Grover’s search algorithm, Shor’s factoring algorithm.

(4 hrs) Principles of information security, classical versus quantum cryptography and key distribution basics, current challenges and future directions in quantum technologies and quantum computing.

To impart knowledge on
Provide students with foundational knowledge of quantum mechanics, linear algebra, and quantum information science.

Introduce the principles of quantum computation and the essential differences between classical and quantum systems.

Introduce algorithms that are simple yet demonstrate quantum speed-up.

To impart an understanding of quantum information theory, including quantum teleportation, superdense coding, and quantum cryptography.

Provide understanding of real-world quantum computing technologies.

Upon successful completion of the course,
CO1. The students will gain an overall understanding on the fundamental principles of quantum mechanics and their application in quantum computation.

CO2. The students will obtain knowledge on description and implementation of quantum gates, circuits, and simple quantum algorithms such as Deutsch-Jozsa, Bernstein-Vazirani, and Simon's algorithm.

CO3. The students will be able to appreciate the significance of quantum correlations in comparison of classical correlations useful for quantum speed-ups.

CO4. The students will demonstrate knowledge of quantum information protocols, including quantum teleportation, superdense coding, and quantum key distribution.

CO5. The students will be able to identify and discuss some aspects of physical realizations of quantum computers and their associated challenges.

A., & Chuang, I. L., , Quantum Computation and Quantum Information, Cambridge University Press (2010).

Parag K. Lala, Quantum Computing: A Beginner's Introduction, McGraw-Hill Education, 1st Edition (2019).

Preskill, J., Lecture Notes on Quantum Computation, https://www.lorentz.leidenuniv.nl/quantumcomputers/literature/preskill_1_to_6.pdf.

G. Benenti, G. Casati, D. Rossini, G. Strini, Principles of Quantum Computation and Information: A Comprehensive Textbook, World Scientific Publishing Co Pte Ltd (2019).