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Lecture
Shor Algorithm: Period Finding
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Factoring Polynomials: Complexity and Algorithms
Delves into the complexity of factoring polynomials and the implications for security.
Polynomial Equations: Solving Methods
Covers various methods for solving polynomial equations through examples.
Shor Algorithm: Circuit Details II
Explores the Shor algorithm circuit details for efficient number factoring using quantum computing.
Integers: Well Ordering and Induction
Explores well ordering, induction, Euclidean division, and prime factorization in integers.
Fundamental Theorem of Arithmetic
Covers prime numbers, unique decomposition of natural numbers into prime factors, and practical implications for calculations.
Introduction: Course syllabus
Introduces the course syllabus, grading scheme, and classical and quantum computation models.
Quantum Measurement Analysis
Explores quantum measurement analysis, including the Simon problem and geometric analogies.
Mathematical Parenthesis on Groups and Lagrange Theorem
Explores cosets in commutative groups, Lagrange theorem, and integer factorization.
Introduction to Algorithms
Covers the concept of algorithms, loop invariants, and examples of algorithmic problem-solving.
Quantum Computing: Fundamentals and Applications
Explores quantum computing fundamentals, qubit control, communication security, and quantum Fourier transform applications.