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Lecture
Shor Algorithm: Period Finding
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Shor Algorithm: Quantum Factorization
Explores the Shor algorithm for quantum factorization and its application in finding function periods.
Polynomials: Roots and Factorization
Explores polynomial roots, factorization, and the Euclidean algorithm in depth.
Shor Algorithm: Circuit Details
Covers the details of the Shor algorithm circuit and its complexity.
Shor's factoring algorithm: Quantum Phase Estimation
Covers Shor's factoring algorithm and the link between order finding and factoring.
Number Theory: GCD and LCM
Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.
Number Theory: GCD and LCM
Covers GCD, LCM, and the Euclidean algorithm for efficient computation.
Lenstra's Algorithm: Integer Factorization
Covers Lenstra's Algorithm for integer factorization, which efficiently computes prime factors of an integer.
Polynomial Factorization over Finite Fields
Introduces polynomial factorization over finite fields and efficient computation of greatest common divisors of polynomials.
Number Theory: Greatest Common Divisor and Prime Factorization
Introduces greatest common divisor, prime factorization, and the Euclidean Algorithm.
Polynomial Factorization: Field Approach
Covers the factorization of polynomials over a field, including division with remainder and common divisors.