Synthesis of Quantum
Circuits vs. Synthesis
of Classical Reversible
Circuits
Alexis De Vos
Stijn De Baerdemacker
Yvan Van Rentergem
Series Editor: Mitchell A. ornton, Southern Methodist University
Synthesis of Quantum Circuits vs.
Synthesis of Classical Reversible Circuits
Alexis De Vos, Universiteit Gent
Stijn De Baerdemacker, Universiteit Gent
Yvan Van Rentergem, Universiteit Gent
At rst sight, quantum computing is completely dierent 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 × n
unitary matrix with n=2
w
, a reversible classical circuit, acting on w bits, is described by a 2
w
×
2
w
permutation matrix. e permutation matrices are studied in group theory of nite groups
(in particular the symmetric group S
n
); 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.
Series ISSN: 1932-3166
About SYNTHESIS
This volume is a printed version of a work that appears in the Synthesis
Digital Library of Engineering and Computer Science. Synthesis
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DE VOS • ET AL
SYNTHESIS OF QUANTUM CIRCUITS VS. SYNTHESIS OF CLASSICAL REVERSIBLE CIRCUITS MORGAN & CLAYPOOL
Synthesis of
Quantum Circuits
vs.
Synthesis of
Classical Reversible Circuits
Synthesis Lectures on Digital
Circuits and Systems
Editor
Mitchell A. ornton, Southern Methodist University
e Synthesis Lectures on Digital Circuits and Systems series is comprised of 50- to 100-page books
targeted for audience members with a wide-ranging background. e Lectures include topics that
are of interest to students, professionals, and researchers in the area of design and analysis of digital
circuits and systems. Each Lecture is self-contained and focuses on the background information
required to understand the subject matter and practical case studies that illustrate applications. e
format of a Lecture is structured such that each will be devoted to a specific topic in digital circuits
and systems rather than a larger overview of several topics such as that found in a comprehensive
handbook. e Lectures cover both well-established areas as well as newly developed or emerging
material in digital circuits and systems design and analysis.
Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits
Alexis De Vos, Stijn De Baerdemacker, and Yvan Van Rentergem
2017
Boolean Differential Calculus
Bernd Steinbach and Christian Posthoff
2017
Embedded Systems Design with Texas Instruments MSP432 32-bit Processor
Dung Dang, Daniel J. Pack, and Steven F. Barrett
2016
Fundamentals of Electronics: Book 4 Oscillators and Advanced Electronics Topics
omas F. Schubert and Ernest M. Kim
2016
Fundamentals of Electronics: Book 3 Active Filters and Amplifier Frequency
omas F. Schubert and Ernest M. Kim
2016
Bad to the Bone: Crafting Electronic Systems with BeagleBone and BeagleBone Black,
Second Edition
Steven F. Barrett and Jason Kridner
2015
iii
Fundamentals of Electronics: Book 2 Amplifiers: Analysis and Design
omas F. Schubert and Ernest M. Kim
2015
Fundamentals of Electronics: Book 1 Electronic Devices and Circuit Applications
omas F. Schubert and Ernest M. Kim
2015
Applications of Zero-Suppressed Decision Diagrams
Tsutomu Sasao and Jon T. Butler
2014
Modeling Digital Switching Circuits with Linear Algebra
Mitchell A. ornton
2014
Arduino Microcontroller Processing for Everyone! ird Edition
Steven F. Barrett
2013
Boolean Differential Equations
Bernd Steinbach and Christian Posthoff
2013
Bad to the Bone: Crafting Electronic Systems with BeagleBone and BeagleBone Black
Steven F. Barrett and Jason Kridner
2013
Introduction to Noise-Resilient Computing
S.N. Yanushkevich, S. Kasai, G. Tangim, A.H. Tran, T. Mohamed, and V.P. Shmerko
2013
Atmel AVR Microcontroller Primer: Programming and Interfacing, Second Edition
Steven F. Barrett and Daniel J. Pack
2012
Representation of Multiple-Valued Logic Functions
Radomir S. Stankovic, Jaakko T. Astola, and Claudio Moraga
2012
Arduino Microcontroller: Processing for Everyone! Second Edition
Steven F. Barrett
2012
Advanced Circuit Simulation Using Multisim Workbench
David Báez-López, Félix E. Guerrero-Castro, and Ofelia Delfina Cervantes-Villagómez
2012
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