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Dancing with Qubits - Second Edition

You're reading from  Dancing with Qubits - Second Edition

Product type Book
Published in Mar 2024
Publisher Packt
ISBN-13 9781837636754
Pages 684 pages
Edition 2nd Edition
Languages
Author (1):
Robert S. Sutor Robert S. Sutor
Profile icon Robert S. Sutor

Table of Contents (26) Chapters

Preface I Foundations
Why Quantum Computing They’re Not Old, They’re Classics More Numbers Than You Can Imagine Planes and Circles and Spheres, Oh My Dimensions 6 What Do You Mean “Probably”? II Quantum Computing
One Qubit Two Qubits, Three Wiring Up the Circuits From Circuits to Algorithms Getting Physical III Advanced Topics
Considering NISQ Algorithms Introduction to Quantum Machine Learning Questions about the Future Afterword
A Quick Reference B Notices C Production Notes Other Books You May Enjoy
References
Index
Appendices

10.7 Shor’s factoring algorithm

We now have the tools we need for Shor’s factoring algorithm to factor integers in polynomial time on a sufficiently large quantum computer. The is a near-exponential improvement over the best known classical methods we described in section 10.2. algorithm$Shor’s factoring Shor’s factoring algorithm factoring$Shor’s algorithm

The complete algorithm has both classical and quantum components. Work is done on both kinds of machines to get to the answer. The quantum portion drops us down to polynomial complexity in the number of gates using phase estimation, order finding, modular exponentiation, and the QFT.

Let odd M in Z be greater than 3 for which you have already tried the basic tricks from section 10.2.3 to check that it is not a multiple of 3, 5, 7, and so on. So that you don’t waste your time, you should also try trial division using a small list of primes, although this is not necessary...

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