Quantum computation and quantum information

This course provides a rigorous introduction to quantum computation and quantum information theory, emphasizing algorithmic, complexity-theoretic, and cryptographic perspectives. Students will study quantum circuits, universal gate sets, and foundational quantum algorithms, including the quantum Fourier transform, phase estimation, and quantum search. The course explores the computational power of quantum algorithms through order finding, factoring, discrete logarithms, Grover’s algorithm, random walks and Hamiltonians, and linear algebraic algorithms complemented by hands-on implementation using Qiskit. A formal introduction to quantum complexity theory is included, focusing on the class BQP and its relationship to classical complexity classes such as P, NP, and PSPACE. The course further develops classical and quantum information-theoretic foundations, covering entropy, source coding, and fundamental limits on information processing, and extends these concepts to the quantum setting through von Neumann entropy, the Holevo bound, Schumacher compression, and coherent information. Building on these principles, the course examines quantum cryptographic protocols, including quantum key distribution (a most remarkable application of quantum information) and quantum secret sharing, highlighting information-theoretic security in the presence of quantum adversaries.

Data Structures and Algorithms; Linear Algebra; Probability and Statistics; Discrete Mathematics

• Linear algebra review (Lectures 1 and 2)
• Postulates of quantum mechanics (Lectures 3,4,5)
• Basics of quantum computation (Lecture 6)

1. Quantum Computation and Quantum Information. Michael A. Nielsen and Isaac L. Chuang. Cambridge.
2. Lecture notes.

• All students are expected to follow a high ethical standard.
• Collaborations and discussions are encouraged. However, all students are required to write up all solutions and submitted work entirely on their own. Any collaboration, or help taken, must be declared. All submissions must include a declaration of originality.
• Students are encouraged to refer to books, papers, internet resources and tools like ChatGPT. They may even consult other individuals. However, the source must be clearly cited if any part of the solution (or even an idea) is taken from such a source.
• Failure to declare any help taken will be interpreted as academic misconduct and result in a F grade in the course.

• Class tests (3): 45%
• Midterm assessment: 20%
• Final assessment: 30%
• Class participation: 5%