Format:
1 Online-Ressource (xv, 109 Seiten)
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Illustrationen
ISBN:
1681733803
,
9781681733807
Series Statement:
Synthesis lectures on digital circuits and systems #54
Content:
At first sight, quantum computing is completely different from classical computing. Nevertheless, a link is provided by reversible computation. Whereas an arbitrary quantum circuit, acting on w qubits, is described by an n x n unitary matrix with n = 2w, a reversible classical circuit, acting on w bits, is described by a 2w x 2w permutation matrix. The permutation matrices are studied in group theory of finite groups (in particular the symmetric group Sn); the unitary matrices are discussed in group theory of continuous groups (a.k.a. Lie groups, in particular the unitary group U(n)). Both the synthesis of a reversible logic circuit and the synthesis of a quantum logic circuit take advantage of the decomposition of a matrix: the former of a permutation matrix, the latter of a unitary matrix. In both cases the decomposition is into three matrices. In both cases the decomposition is not unique
Content:
Dual DecompositionSynthesis 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
Content:
Dual DecompositionConclusion; Polar Decomposition; Bibliography; Authors' Biographies; Index; Blank Page
Content:
Intro; 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
Note:
Includes bibliographical references (pages 99-104) and index
Additional Edition:
ISBN 9781681733791
Additional Edition:
ISBN 9781681733814
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031798962
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031798948
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031798979
Language:
English
DOI:
10.1007/978-3-031-79895-5
Author information:
De Vos, Alexis
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