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Lecture
Shor's Factoring Algorithm
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Introduction: Course syllabus
Introduces the course syllabus, grading scheme, and classical and quantum computation models.
Complex Numbers: Gauss Numbers
Explores Gaussian integers, prime factorization, and number theory concepts related to prime numbers.
Quantum and Nanocomputing
Explores quantum computing fundamentals, quantum Fourier transform, RSA encryption, Shor's algorithm, and experimental implementations.
Integer Factorization: Methods and Algorithms
Explores methods and algorithms for integer factorization, including testing for B smoothness and computing small primes.
Shor Algorithm: Quantum Factorization
Covers the Shor algorithm for quantum factorization using tensor methods and graded solutions.
Rudiments of Number Theory
Introduces modulo arithmetic, Euclid's algorithm, and congruence in number theory.
Integers: Well Ordering and Induction
Explores well ordering, induction, Euclidean division, and prime factorization in integers.
Untitled
Algebraic Structures: Groups and Rings
Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.
Lenstra's Algorithm: Integer Factorization
Covers Lenstra's Algorithm for integer factorization, which efficiently computes prime factors of an integer.