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Acknowledgments
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Acknowledgments
by Mitchell A. Thornton, Yvan Van Rentergem, Stijn De Baerdemacker, Alexis De Vos
Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits
Acknowledgments
Introduction
Conventional Computing
Boolean Functions of One Variable
Boolean Functions of Two Variables
Boolean Functions of n Variables
The Minterm Expansion
The Reed–Muller Expansion
The Minimal ESOP Expansion
Group Theory
Reversible Computing
Permutation Groups
A Permutation Decomposition
Matrix Groups
Subgroups
Young Subgroups
Quantum Computing
Bottom-Up vs. Top-Down
Bottom
The Group S_2
Two Important Young Subgroups of S_2w
Controlled Circuits
Controlled NOT Gates
Controlled Circuits vs. Controlled Gates
Primal Decomposition
Dual Decomposition
Synthesis Efficiency
Refined Synthesis Algorithm
Examples
Variable Ordering
Bottom-Up
The Square Root of the NOT
One-(qu)bit Calculations
Two and Multi-(qu)bit Calculations
More Roots of NOT
NEGATORs
NEGATOR Circuits
The Group ZU(n)
The Group XU(n)
A Matrix Decomposition
Group Hierarchy
Top
Preliminary Circuit Decomposition
Primal Decomposition
Group Structure
Dual Decomposition
Detailed Procedure
Examples
Synthesis Efficiency
Further Synthesis
An Extra Decomposition
Top-Down
Top vs. Bottom
Light Matrices
Primal Decomposition
Group Hierarchy
Dual Decomposition
Conclusion
Polar Decomposition
Bibliography (1/2)
Bibliography (2/2)
Authors' Biographies
Index
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