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Synthesis of quantum circuits vs. synthesis of classical reversible circuits /

Bibliographic Details
Main Authors: Vos, Alexis de (Author), De Baerdemacker, Stijn (Author), Van Rentergem, Yvan (Author)
Corporate Author: Morgan & Claypool Publishers
Format: eBook
Language:English
Published: [San Rafael, California] : Morgan & Claypool, 2018.
Series:Synthesis digital library of engineering and computer science.
Synthesis lectures on digital circuits and systems ; # 54.
Subjects:
Computers > Circuits.
Logic circuits.
Quantum computing.
Reversible computing.
circuit synthesis
group theory
matrix decomposition
permutation matrix
quantum computing
reversible computing
unitary matrix
Electronic books.
Online Access:Connect to the full text of this electronic book (PDF)
Table of Contents:
  • 1. Introduction
  • 1.1 Conventional computing
  • 1.2 Boolean functions of one variable
  • 1.3 Boolean functions of two variables
  • 1.4 Boolean functions of n variables
  • 1.4.1 The minterm expansion
  • 1.4.2 The Reed-Muller expansion
  • 1.4.3 The minimal ESOP expansion
  • 1.5 Group theory
  • 1.6 Reversible computing
  • 1.7 Permutation groups
  • 1.8 A permutation decomposition
  • 1.9 Matrix groups
  • 1.10 Subgroups
  • 1.11 Young subgroups
  • 1.12 Quantum computing
  • 1.13 Bottom-up vs. top-down
  • 2. Bottom
  • 2.1 The group S2
  • 2.2 Two important young subgroups of S2w
  • 2.2.1 Controlled circuits
  • 2.2.2 Controlled NOT gates
  • 2.2.3 Controlled circuits vs. controlled gates
  • 2.3 Primal decomposition
  • 2.4 Dual decomposition
  • 2.5 Synthesis efficiency
  • 2.6 Refined synthesis algorithm
  • 2.7 Examples
  • 2.8 Variable ordering
  • 3. Bottom-up
  • 3.1 The square root of the NOT
  • 3.1.1 One-(qu)bit calculations
  • 3.1.2 Two and multi-(qu)bit calculations
  • 3.2 More roots of NOT
  • 3.3 NEGATORs
  • 3.4 NEGATOR circuits
  • 3.5 The group ZU(n)
  • 3.6 The group XU(n)
  • 3.7 A matrix decomposition
  • 3.8 Group hierarchy
  • 4. Top
  • 4.1 Preliminary circuit decomposition
  • 4.2 Primal decomposition
  • 4.3 Group structure
  • 4.4 Dual decomposition
  • 4.5 Detailed procedure
  • 4.6 Examples
  • 4.7 Synthesis efficiency
  • 4.8 Further synthesis
  • 4.9 An extra decomposition
  • 5. Top-down
  • 5.1 Top vs. bottom
  • 5.2 Light matrices
  • 5.3 Primal decomposition
  • 5.4 Group hierarchy
  • 5.5 Dual decomposition
  • 6. Conclusion
  • A. Polar decomposition
  • Bibliography
  • Authors' biographies
  • Index.