Related lectures (23)
Introduction: Course syllabus
Introduces the course syllabus, grading scheme, and classical and quantum computation models.
Shor's algorithm: factoring integers
Covers the basics of Shor's algorithm for factoring integers and the steps involved in the quantum algorithm.
Mathematical Parenthesis on Groups and Lagrange Theorem
Explores cosets in commutative groups, Lagrange theorem, and integer factorization.
Shor's algorithm: quantum circuit
Covers the implementation of Shor's algorithm on a quantum circuit, including the analysis of quantum Fourier transform.
Hidden Sub-group Problem and Simon Algorithm
Explores the hidden subgroup problem and the Simon algorithm in quantum computing.
Subgroups and Cosets: Lagrange's Theorem
Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.
Homological Algebra: Exact Sequences
Covers exact sequences in homological algebra and the properties of Hom functors.
Closest Vector Problem: Voronoi Cells
Explores the Closest Vector Problem and Voronoi cells in lattice reduction algorithms.
Partial Derivatives: Definitions and Applications
Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.
Long Exact Sequence of Ext-Modules
Explores the long exact sequence of Ext-modules and their computations in homological algebra.

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