Syllabus

Introduction to quantum mechanics, wave-particle duality, double-slit experiment, photoelectric effect, linear algebra: vectors, matrices, inner products, Hermitian operators, state vectors, superposition, and Dirac notation, postulates of quantum mechanics: state space, observables, measurement, and time evolution of quantum states.

Classical vs. quantum particle in a box, quantization of energy levels, potential wells: finite, and step potentials, classical vs. quantum harmonic oscillator, zero-point energy, orbital angular momentum, spin angular momentum, bosons and fermions.

Basics of statistical mechanics, microstates and macrostates, ensembles, postulate of equal a priori probabilities, Boltzmann factor, partition function, example two-Level system, thermal equilibrium and Gibbs principle, ideal gas: partition function and thermodynamic quantities, Fermi-Dirac and Bose-Einstein distributions, indistinguishability of particles, Pauli exclusion principle, Fermi-Dirac: Electron gas in metals, Bose-Einstein statistics: blackbody radiation.

Classical vs. quantum Information, Born rule, no-cloning theorem, single qubit gates: Pauli-X, Pauli-Y, Pauli-Z, Hadamard gate, CNOT gate, SWAP gate, entanglement generation using CNOT, quantum circuits, universality of quantum gates, quantum entanglement and uses in quantum algorithms, quantum speed-up, decoherence, noise, and errors, basics of quantum error correction, threshold theorem and error correction overhead, brief introduction to entanglement entropy and mutual information.

Introduction to Turing machine, computational complexity, complexity classes, P vs. NP problem, advanced computational complexity: NP-completeness, PSPACE, EXP, quantum Turing machine, components of a quantum Turing machine, quantum complexity classes: BQP, QMA, quantum vs. classical classes, quantum supremacy, post-quantum cryptography.

Provide students with foundational knowledge of quantum mechanics, linear algebra, and quantum information science to better understand quantum technology’s basics.

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

To impart an understanding of quantum information theory basics.

Provide understanding of real-world quantum computing technologies.

The students will gain an overall understanding of the fundamental principles of quantum mechanics and their application in quantum computation.

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

The students will be able to demonstrate knowledge of quantum information protocols, including quantum key distribution.

The students will be able to identify and discuss different complexities of quantum or classical problems.

Nouredine Zettili, Quantum Mechanics: Concepts and Applications, Wiley , (2009)

R. K. Pathria, Statistical Mechanics, Butterworth-Heinemann , (2016)

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

David J. Griffiths, Introduction to Quantum Mechanics (3rd edition), Cambridge University Press , (2024)

L. D. Landau, E. M. Lifshitz, Statistical Physics: Volume 5 (3rd edition), Elsevier , (2013)

Robert S. Sutor, Dancing with Qubits: How Quantum Computing Works and how it Can Change the World, Packt Publishing , (2019)

J. J. Sakurai, Modern Quantum Mechanics (revised edition), Addision-Wesley publication company , (1994)

R. Shankar, Principles of Quantum Mechanics (2nd edition), Springer , (1994)

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