Learn about phase estimation and its application to quantum factoring in this comprehensive video lecture from the Understanding Quantum Information & Computation series. Explore the mathematical foundations of phase estimation, including the spectral theorem and quantum Fourier transform, before diving into its practical implementation. Master the connection between phase estimation and the order-finding problem, which forms the basis of Shor's groundbreaking quantum factoring algorithm. Discover how to efficiently implement quantum circuits for these algorithms, with detailed explanations of phase kickback, control qubits, and eigenvector analysis. Access additional learning materials including Qiskit implementations, written content, and PDF slides through IBM Quantum Learning platform to enhance your understanding of these fundamental quantum computing concepts.
Phase Estimation and Factoring: Understanding Quantum Information and Computation - Lesson 7
Overview
Syllabus
— Introduction
— Overview
— Spectral theorem
— Phase estimation problem
— Warm-up: using phase kickback
— Iterating the unitary operation
— Two control qubits
— Two-qubit phase estimation
— Quantum Fourier transform
— Circuits for the QFT
— Phase estimation procedure
— The order-finding problem
— Order-finding by phase-estimation
— Eigenvectors and eigenvalues
— A convenient eigenvector
— A random eigenvector
— Implementation
— Factoring through order-finding
— Conclusion
Taught by
Qiskit
