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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 ?? qubits, is described by an ?? × ?? unitary matrix with ??=2??, a reversible classical circuit, acting on ?? bits, is described by a 2?? × 2?? permutation matrix. The permutation matrices are studied in group theory of finite groups (in particular the symmetric group ????); the unitary matrices are discussed in group theory of continuous groups (a.k.a. Lie groups, in particular the unitary group U(??)). 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.
Book Synopsis Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits by : Alexis De Vos
Download or read book Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits written by Alexis De Vos and published by Morgan & Claypool Publishers. This book was released on 2018-07-03 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ?? qubits, is described by an ?? × ?? unitary matrix with ??=2??, a reversible classical circuit, acting on ?? bits, is described by a 2?? × 2?? permutation matrix. The permutation matrices are studied in group theory of finite groups (in particular the symmetric group ????); the unitary matrices are discussed in group theory of continuous groups (a.k.a. Lie groups, in particular the unitary group U(??)). 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.
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 ?? qubits, is described by an ?? × ?? unitary matrix with ??=2??, a reversible classical circuit, acting on ?? bits, is described by a 2?? × 2?? permutation matrix. The permutation matrices are studied in group theory of finite groups (in particular the symmetric group ????); the unitary matrices are discussed in group theory of continuous groups (a.k.a. Lie groups, in particular the unitary group U(??)). 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.
Book Synopsis Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits by : Alexis De Vos
Download or read book Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits written by Alexis De Vos and published by Springer Nature. This book was released on 2022-05-31 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ?? qubits, is described by an ?? × ?? unitary matrix with ??=2??, a reversible classical circuit, acting on ?? bits, is described by a 2?? × 2?? permutation matrix. The permutation matrices are studied in group theory of finite groups (in particular the symmetric group ????); the unitary matrices are discussed in group theory of continuous groups (a.k.a. Lie groups, in particular the unitary group U(??)). 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.
For the first time in book form, this comprehensive and systematic monograph presents methods for the reversible synthesis of logic functions and circuits. It is illustrated with a wealth of examples and figures that describe in detail the systematic methodologies of synthesis using reversible logic.
Book Synopsis Reversible Logic Synthesis by : Anas N. Al-Rabadi
Download or read book Reversible Logic Synthesis written by Anas N. Al-Rabadi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time in book form, this comprehensive and systematic monograph presents methods for the reversible synthesis of logic functions and circuits. It is illustrated with a wealth of examples and figures that describe in detail the systematic methodologies of synthesis using reversible logic.
"Over the last few years, research on reversible logic emerged as an important topic in many directions starting from synthesis towards test, debugging and verification as well as arithmetic designs. The motivation behind reversible computation comes from low power dissipation and close relation to quantum circuits, which, in the near future, could become a competitor to current classical circuits. As reversible circuits are still relatively new, the biggest research impact is on synthesis of such circuits. In the first part of this thesis, we present a synthesis approach to realize large reversible circuits based on classical technology mapping. The irreversible nature of most of the original algorithms makes the synthesis of reversible circuits from irreversible specifications a challenging task. A large part of the existing algorithms, although optimized in garbage bits and gate counts, are restricted to small functions, while some approaches address large functions but are costly in terms of gate count, additional lines and quantum cost. A synthesis solution for large circuits with less quantum cost and garbage bits is presented in this thesis by avoiding permutation based reversible embedding.In addition, we present an indirect way of realizing arithmetic circuits avoiding the direct translation of classical truth table with better performance with respect to various reversible parameters. We develop an improved reversible controlled adder/subtractor with overflow detection to enhance reliability. We use this adder/subtractor module with slight modification to implement some complex designs such as reversible square-root circuit, comparator for signed numbers and finally a new integrated module of reversible arithmetic logic unit, which encapsulates most of the operations in classical realization with less number of control lines. This module intends to perform the basic mathematical operations of addition, subtraction with overflow detection, comparison, as well as logic operations AND, OR, XOR and some negated logical functions such as NAND, NOR and XNOR including implication. Thus our design is very efficient and versatile with less number of lines and quantum cost.Apart from synthesis and designs, testing must also be brought onboard to accommodate the reliable implementation of reversible logic. Our final part of the thesis addresses this issue. To date, most reversible circuit fault models include stuck-at-value, missing gate fault and control point faults of Toffoli network. Now-a-days, the synthesis process is not restricted to standard reversible gates, rather some designs especially arithmetic circuits include other gates. In such realization, failures can happen due to erroneous replacements or incorrect cascading of gates, which cannot be defined with existing fault model alone. Thus in this thesis, we present two fault models namely gate replacement fault and wire replacement fault which target circuits implemented using any reversible gate library. To test such faults, three testing schemes are proposed by adopting the conventional testing methods for irreversible circuits based on Boolean Satisfiability (SAT) formulation. In particular, a new Reversible Test Miter is constructed, which, along with backtracking, speed up detection gate and wire replacement faults with less memory. In addition, on a different study, the testing feature of modular reversible design is investigated and presented in this thesis showing that the same test set of basic block is applicable for cascaded design. We hope our effort on synthesis, design and test of reversible circuits will enrich their viable technological realization." --
Book Synopsis Synthesis, Design and Test of Reversible Circuits Employing Classical Techniques by : Sayeeda Sultana
Download or read book Synthesis, Design and Test of Reversible Circuits Employing Classical Techniques written by Sayeeda Sultana and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Over the last few years, research on reversible logic emerged as an important topic in many directions starting from synthesis towards test, debugging and verification as well as arithmetic designs. The motivation behind reversible computation comes from low power dissipation and close relation to quantum circuits, which, in the near future, could become a competitor to current classical circuits. As reversible circuits are still relatively new, the biggest research impact is on synthesis of such circuits. In the first part of this thesis, we present a synthesis approach to realize large reversible circuits based on classical technology mapping. The irreversible nature of most of the original algorithms makes the synthesis of reversible circuits from irreversible specifications a challenging task. A large part of the existing algorithms, although optimized in garbage bits and gate counts, are restricted to small functions, while some approaches address large functions but are costly in terms of gate count, additional lines and quantum cost. A synthesis solution for large circuits with less quantum cost and garbage bits is presented in this thesis by avoiding permutation based reversible embedding.In addition, we present an indirect way of realizing arithmetic circuits avoiding the direct translation of classical truth table with better performance with respect to various reversible parameters. We develop an improved reversible controlled adder/subtractor with overflow detection to enhance reliability. We use this adder/subtractor module with slight modification to implement some complex designs such as reversible square-root circuit, comparator for signed numbers and finally a new integrated module of reversible arithmetic logic unit, which encapsulates most of the operations in classical realization with less number of control lines. This module intends to perform the basic mathematical operations of addition, subtraction with overflow detection, comparison, as well as logic operations AND, OR, XOR and some negated logical functions such as NAND, NOR and XNOR including implication. Thus our design is very efficient and versatile with less number of lines and quantum cost.Apart from synthesis and designs, testing must also be brought onboard to accommodate the reliable implementation of reversible logic. Our final part of the thesis addresses this issue. To date, most reversible circuit fault models include stuck-at-value, missing gate fault and control point faults of Toffoli network. Now-a-days, the synthesis process is not restricted to standard reversible gates, rather some designs especially arithmetic circuits include other gates. In such realization, failures can happen due to erroneous replacements or incorrect cascading of gates, which cannot be defined with existing fault model alone. Thus in this thesis, we present two fault models namely gate replacement fault and wire replacement fault which target circuits implemented using any reversible gate library. To test such faults, three testing schemes are proposed by adopting the conventional testing methods for irreversible circuits based on Boolean Satisfiability (SAT) formulation. In particular, a new Reversible Test Miter is constructed, which, along with backtracking, speed up detection gate and wire replacement faults with less memory. In addition, on a different study, the testing feature of modular reversible design is investigated and presented in this thesis showing that the same test set of basic block is applicable for cascaded design. We hope our effort on synthesis, design and test of reversible circuits will enrich their viable technological realization." --
This book opens the door to a new interesting and ambitious world of reversible and quantum computing research. It presents the state of the art required to travel around that world safely. Top world universities, companies and government institutions are in a race of developing new methodologies, algorithms and circuits on reversible logic, quantum logic, reversible and quantum computing and nano-technologies. In this book, twelve reversible logic synthesis methodologies are presented for the first time in a single literature with some new proposals. Also, the sequential reversible logic circuitries are discussed for the first time in a book. Reversible logic plays an important role in quantum computing. Any progress in the domain of reversible logic can be directly applied to quantum logic. One of the goals of this book is to show the application of reversible logic in quantum computing. A new implementation of wavelet and multiwavelet transforms using quantum computing is performed for this purpose. Researchers in academia or industry and graduate students, who work in logic synthesis, quantum computing, nano-technology, and low power VLSI circuit design, will be interested in this book.
Book Synopsis Reversible Logic Synthesis Methodologies with Application to Quantum Computing by : Saleem Mohammed Ridha Taha
Download or read book Reversible Logic Synthesis Methodologies with Application to Quantum Computing written by Saleem Mohammed Ridha Taha and published by Springer. This book was released on 2015-09-24 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book opens the door to a new interesting and ambitious world of reversible and quantum computing research. It presents the state of the art required to travel around that world safely. Top world universities, companies and government institutions are in a race of developing new methodologies, algorithms and circuits on reversible logic, quantum logic, reversible and quantum computing and nano-technologies. In this book, twelve reversible logic synthesis methodologies are presented for the first time in a single literature with some new proposals. Also, the sequential reversible logic circuitries are discussed for the first time in a book. Reversible logic plays an important role in quantum computing. Any progress in the domain of reversible logic can be directly applied to quantum logic. One of the goals of this book is to show the application of reversible logic in quantum computing. A new implementation of wavelet and multiwavelet transforms using quantum computing is performed for this purpose. Researchers in academia or industry and graduate students, who work in logic synthesis, quantum computing, nano-technology, and low power VLSI circuit design, will be interested in this book.
This dissertation is devoted to efficient automated logic synthesis of reversible circuits using various gate types and initial specifications. These Reversible circuits are of interest to several modern technologies, including Nanotechnology, Quantum computing, Quantum Dot Cellular Automata, Optical computing and low power adiabatic CMOS, but so far the most important practical application of reversible circuits is in quantum computing. Logic synthesis methodologies for reversible circuits are very different than those for classical CMOS or other technologies. The focus of this dissertation is on synthesis of reversible (permutative) binary circuits. It is not related to general unitary circuits that are used in quantum computing and which exhibit quantum mechanical phenomena such as superposition and entanglement. The interest in this dissertation is only in logic synthesis aspects and not in physical (technological) design aspects of reversible circuits. Permutative quantum circuits are important because they include the class of oracles and blocks that are parts of oracles, such as comparators or arithmetic blocks, counters of ones, etc. Every practical quantum algorithm, such as the Grover Algorithm, has many permutative circuits. These circuits are also used in Shor Algorithm (integer factorization), simulation of quantum systems, communication and many other quantum algorithms. Designing permutative circuits is therefore the major engineering task that must be solved to practically realize a quantum algorithm. The dissertation presents the theory that leads to MP (Multi-Path) algorithm, which is currently the top minimizer of reversible circuits with no ancilla bits. Comparison of MP with other 2 leading software tools is done. This software allows to minimize functions of more variables and with smaller quantum cost that other CAD tools. Other software developed in this dissertation allows to synthesize reversible circuits for functions with "don't cares" in their initial specifications. Theory to realize functions from relational representations is also given. Our yet other software tool allows to synthesize reversible circuits for new types of reversible logic, for which no algorithm was ever created, using the so-called "pseudo-reversible" gates called Y-switches.
Book Synopsis Synthesis of Reversible Functions Using Various Gate Libraries and Design Specifications by : Nouraddin Alhagi
Download or read book Synthesis of Reversible Functions Using Various Gate Libraries and Design Specifications written by Nouraddin Alhagi and published by . This book was released on 2010 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is devoted to efficient automated logic synthesis of reversible circuits using various gate types and initial specifications. These Reversible circuits are of interest to several modern technologies, including Nanotechnology, Quantum computing, Quantum Dot Cellular Automata, Optical computing and low power adiabatic CMOS, but so far the most important practical application of reversible circuits is in quantum computing. Logic synthesis methodologies for reversible circuits are very different than those for classical CMOS or other technologies. The focus of this dissertation is on synthesis of reversible (permutative) binary circuits. It is not related to general unitary circuits that are used in quantum computing and which exhibit quantum mechanical phenomena such as superposition and entanglement. The interest in this dissertation is only in logic synthesis aspects and not in physical (technological) design aspects of reversible circuits. Permutative quantum circuits are important because they include the class of oracles and blocks that are parts of oracles, such as comparators or arithmetic blocks, counters of ones, etc. Every practical quantum algorithm, such as the Grover Algorithm, has many permutative circuits. These circuits are also used in Shor Algorithm (integer factorization), simulation of quantum systems, communication and many other quantum algorithms. Designing permutative circuits is therefore the major engineering task that must be solved to practically realize a quantum algorithm. The dissertation presents the theory that leads to MP (Multi-Path) algorithm, which is currently the top minimizer of reversible circuits with no ancilla bits. Comparison of MP with other 2 leading software tools is done. This software allows to minimize functions of more variables and with smaller quantum cost that other CAD tools. Other software developed in this dissertation allows to synthesize reversible circuits for functions with "don't cares" in their initial specifications. Theory to realize functions from relational representations is also given. Our yet other software tool allows to synthesize reversible circuits for new types of reversible logic, for which no algorithm was ever created, using the so-called "pseudo-reversible" gates called Y-switches.
At this time the synthesis of reversible circuits for quantum computing is an active area of research. In the most restrictive quantum computing models there are no ancilla lines and the quantum cost, or latency, of performing a reversible form of the AND gate, or Toffoli gate, increases exponentially with the number of input variables. In contrast, the quantum cost of performing any combination of reversible EXOR gates, or CNOT gates, on n input variables requires at most O(n2/log2n) gates. It was under these conditions that EXOR-AND-EXOR, or EPOE, synthesis was developed. In this work, the GF(2) logic theory used in EPOE is expanded and the concept of an EXOR-AND product transform is introduced. Because of the generality of this logic theory, it is adapted to EXOR-AND-OR, or SPOE, synthesis. Three heuristic spectral logic synthesis algorithms are introduced, implemented in a program called XAX, and compared with previous work in classical logic circuits of up to 26 inputs. Three linear reversible circuit methods are also introduced and compared with previous work in linear reversible logic circuits of up to 100 inputs.
Book Synopsis Synthesis of Linear Reversible Circuits and EXOR-AND-based Circuits for Incompletely Specified Multi-Output Functions by :
Download or read book Synthesis of Linear Reversible Circuits and EXOR-AND-based Circuits for Incompletely Specified Multi-Output Functions written by and published by . This book was released on 2017 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: At this time the synthesis of reversible circuits for quantum computing is an active area of research. In the most restrictive quantum computing models there are no ancilla lines and the quantum cost, or latency, of performing a reversible form of the AND gate, or Toffoli gate, increases exponentially with the number of input variables. In contrast, the quantum cost of performing any combination of reversible EXOR gates, or CNOT gates, on n input variables requires at most O(n2/log2n) gates. It was under these conditions that EXOR-AND-EXOR, or EPOE, synthesis was developed. In this work, the GF(2) logic theory used in EPOE is expanded and the concept of an EXOR-AND product transform is introduced. Because of the generality of this logic theory, it is adapted to EXOR-AND-OR, or SPOE, synthesis. Three heuristic spectral logic synthesis algorithms are introduced, implemented in a program called XAX, and compared with previous work in classical logic circuits of up to 26 inputs. Three linear reversible circuit methods are also introduced and compared with previous work in linear reversible logic circuits of up to 100 inputs.
This book presents a new optimization flow for quantum circuits realization. At the reversible level, optimization algorithms are presented to reduce the quantum cost. Then, new mapping approaches to decompose reversible circuits to quantum circuits using different quantum libraries are described. Finally, optimization techniques to reduce the quantum cost or the delay are applied to the resulting quantum circuits. Furthermore, this book studies the complexity of reversible circuits and quantum circuits from a theoretical perspective.
Book Synopsis Reversible and Quantum Circuits by : Nabila Abdessaied
Download or read book Reversible and Quantum Circuits written by Nabila Abdessaied and published by Springer. This book was released on 2016-06-06 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new optimization flow for quantum circuits realization. At the reversible level, optimization algorithms are presented to reduce the quantum cost. Then, new mapping approaches to decompose reversible circuits to quantum circuits using different quantum libraries are described. Finally, optimization techniques to reduce the quantum cost or the delay are applied to the resulting quantum circuits. Furthermore, this book studies the complexity of reversible circuits and quantum circuits from a theoretical perspective.
This book is about the Arduino microcontroller and the Arduino concept. The visionary Arduino team of Massimo Banzi, David Cuartielles, Tom Igoe, Gianluca Martino, and David Mellis launched a new innovation in microcontroller hardware in 2005, the concept of open-source hardware. Their approach was to openly share details of microcontroller-based hardware design platforms to stimulate the sharing of ideas and promote innovation. This concept has been popular in the software world for many years. In June 2019, Joel Claypool and I met to plan the fourth edition of Arduino Microcontroller Processing for Everyone! Our goal has been to provide an accessible book on the rapidly changing world of Arduino for a wide variety of audiences including students of the fine arts, middle and senior high school students, engineering design students, and practicing scientists and engineers. To make the book more accessible to better serve our readers, we decided to change our approach and provide a series of smaller volumes. Each volume is written to a specific audience. This book, Arduino I: Getting Started is written for those looking for a quick tutorial on the Arduino environment, platforms, interface techniques, and applications. Arduino II will explore advanced techniques, applications, and systems design. Arduino III will explore Arduino applications in the Internet of Things (IoT). Arduino I: Getting Started covers three different Arduino products: the Arduino UNO R3 equipped with the Microchip ATmega328, the Arduino Mega 2560 equipped with the Microchip ATmega2560, and the wearable Arduino LilyPad.
Book Synopsis Arduino I by : Steven F. Barrett
Download or read book Arduino I written by Steven F. Barrett and published by Springer Nature. This book was released on 2022-05-31 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the Arduino microcontroller and the Arduino concept. The visionary Arduino team of Massimo Banzi, David Cuartielles, Tom Igoe, Gianluca Martino, and David Mellis launched a new innovation in microcontroller hardware in 2005, the concept of open-source hardware. Their approach was to openly share details of microcontroller-based hardware design platforms to stimulate the sharing of ideas and promote innovation. This concept has been popular in the software world for many years. In June 2019, Joel Claypool and I met to plan the fourth edition of Arduino Microcontroller Processing for Everyone! Our goal has been to provide an accessible book on the rapidly changing world of Arduino for a wide variety of audiences including students of the fine arts, middle and senior high school students, engineering design students, and practicing scientists and engineers. To make the book more accessible to better serve our readers, we decided to change our approach and provide a series of smaller volumes. Each volume is written to a specific audience. This book, Arduino I: Getting Started is written for those looking for a quick tutorial on the Arduino environment, platforms, interface techniques, and applications. Arduino II will explore advanced techniques, applications, and systems design. Arduino III will explore Arduino applications in the Internet of Things (IoT). Arduino I: Getting Started covers three different Arduino products: the Arduino UNO R3 equipped with the Microchip ATmega328, the Arduino Mega 2560 equipped with the Microchip ATmega2560, and the wearable Arduino LilyPad.
The LNCS journal Transactions on Computational Science reflects recent developments in the field of Computational Science, conceiving the field not as a mere ancillary science but rather as an innovative approach supporting many other scientific disciplines. The journal focuses on original high-quality research in the realm of computational science in parallel and distributed environments, encompassing the facilitating theoretical foundations and the applications of large-scale computations and massive data processing. It addresses researchers and practitioners in areas ranging from aerospace to biochemistry, from electronics to geosciences, from mathematics to software architecture, presenting verifiable computational methods, findings, and solutions and enabling industrial users to apply techniques of leading-edge, large-scale, high performance computational methods. This, the 24th issue of the Transactions on Computational Science journal, guest edited by Himanshu Thapliyal and Nagarajan Ranganathan, is devoted to the topic of reversible computing. It is comprised of eight selected papers on reversible energy recovery designs, design of reversible logic gates and arithmetic circuits in optical computing, reversible basic linear algebra subprograms, quantum circuit description language, and reversible circuit and logic synthesis.
Book Synopsis Transactions on Computational Science XXIV by : Marina L. Gavrilova
Download or read book Transactions on Computational Science XXIV written by Marina L. Gavrilova and published by Springer. This book was released on 2014-12-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LNCS journal Transactions on Computational Science reflects recent developments in the field of Computational Science, conceiving the field not as a mere ancillary science but rather as an innovative approach supporting many other scientific disciplines. The journal focuses on original high-quality research in the realm of computational science in parallel and distributed environments, encompassing the facilitating theoretical foundations and the applications of large-scale computations and massive data processing. It addresses researchers and practitioners in areas ranging from aerospace to biochemistry, from electronics to geosciences, from mathematics to software architecture, presenting verifiable computational methods, findings, and solutions and enabling industrial users to apply techniques of leading-edge, large-scale, high performance computational methods. This, the 24th issue of the Transactions on Computational Science journal, guest edited by Himanshu Thapliyal and Nagarajan Ranganathan, is devoted to the topic of reversible computing. It is comprised of eight selected papers on reversible energy recovery designs, design of reversible logic gates and arithmetic circuits in optical computing, reversible basic linear algebra subprograms, quantum circuit description language, and reversible circuit and logic synthesis.
