Classical Quantum Algorithms
Description
Fundamental quantum algorithms that demonstrate quantum computational advantages including search, factoring, and decision algorithms.
Learning Objectives
To master the design, analysis, and implementation of classical quantum algorithms that demonstrate quantum computational advantages over classical approaches. Learners will understand algorithm complexity analysis, implement key quantum algorithms like Deutsch-Jozsa, Shor's factoring algorithm, and Grover's search algorithm, analyze their performance benefits, and understand the theoretical foundations that enable quantum speedups in specific computational problems.
Topics (7)
Comprehensive coverage of QFT including mathematical formulation, quantum circuit implementation, relationship to classical discrete Fourier transform, and its central role in Shor's algorithm and quantum phase estimation.
Detailed study of Shor's algorithm including number theory background, period finding reduction, quantum circuit implementation, post-processing steps, and implications for cryptographic security and RSA encryption.
Comprehensive study of Grover's algorithm including unstructured search problem, amplitude amplification technique, geometric interpretation on Bloch sphere, optimality proof, and applications to various search and optimization problems.
Comprehensive analysis of quantum computational complexity including BQP class characterization, quantum speedup analysis, oracle complexity, quantum query complexity, and theoretical foundations of quantum computational advantages.
Comprehensive study of the Deutsch-Jozsa algorithm including problem formulation, quantum circuit implementation, oracle construction, and analysis of exponential speedup over classical deterministic algorithms for balanced vs constant function determination.
Detailed study of Simon's algorithm including hidden subgroup problem formulation, quantum circuit construction, measurement analysis, and its exponential advantage over classical approaches for period finding in Boolean functions.
Detailed study of quantum phase estimation including eigenvalue estimation, quantum circuit construction, error analysis, precision requirements, and applications in quantum simulation and variational quantum algorithms.