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Table of Contents
1. Quantum Factoring
2. Period Finding
3. Order Finding
4. Factoring
5. Factoring–contd.
6. Using a Fourier Transform
7. Discrete Fourier Transform
8. DFT is Unitary
9. Inverse DFT
10. Quantum Fourier Transform
11. Fourier Transform on Binary Strings
12. Quantum Fourier Transform Circuit
13. Conditional Phase Shifts
14. Preparing the State
15. First Measurement
16. Applying the QFT
17. Second Measurement
18. Exponentiation
19. Some Points to Note
Summary
This document discusses various topics related to quantum computing, with a focus on quantum factoring and its implications for cryptography. It covers concepts such as period finding, order finding, and the use of Fourier transforms in quantum algorithms. The document explains how quantum Fourier transform can be implemented efficiently using quantum gates. It also explores the process of preparing states, measurements, and exponentiation in the context of quantum factoring algorithms. The document highlights the probabilistic nature of finding periods in quantum algorithms and emphasizes the importance of repeated trials for success.