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Quantum Computing and Shor's Algorithm
Matthew Hayward
Original Spring 1999, Revised 2015
Contents
Preface
Introduction
The Classical Computer
Turing Machines
Church-Turing Thesis
Running Time and Complexity Classes
The Quantum Computer
Quantum Physics
The Classical Bit
State Vectors and Dirac Notation
Superposition and Eigenstates
The Quantum qubit
The Quantum Memory Register
Probability Interpretation
Quantum Parallelism
The Efficiency of the Quantum Computer
Quantum Algorithms
Introduction to Shor's Algorithm
Motivation for Shor's Algorithm
Overview of Shor's Algorithm
Steps to Shor's Algorithm
Other Quantum Algorithms
A Simulation of Shor's Algorithm on a Classical Computer
Introduction to the Code for the Simulation
The Complex Number Class
The Quantum Memory Register Class
The Simulation of Shor's Algorithm
Utility Functions for the Simulation
Conclusion
Bibliography
Glossary
Mathematics Used in this Paper
Binary Representation of Numbers
Complex Numbers
Vector Mathematics
Actual Quantum Computers and Further Research
Other Quantum Computer Simulators
Code for my Simulation of Shor's Algorithm
complex.h
complex.C
qureg.h
qureg.C
shor.C
util.h
util.C
qubit.C
Sample Output
Sample Output for
n
= 17
Sample Output for
n
= 15
Sample Output for
n
= 33
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Matthew Hayward -
Quantum Computing and Shor's Algorithm GitHub Repository
