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Synthesis Of Quantum Circuits Vs Synthesis Of Classical Reversible Circuits
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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.
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.
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.
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." --
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.
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.
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.
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.
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.
Book Synopsis Reversible Computation by : Jarkko Kari
Download or read book Reversible Computation written by Jarkko Kari and published by Springer. This book was released on 2018-08-30 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Reversible Computation, RC 2018, held in Leicester, UK, in September 2018. The 13 full, 7 short, and one tutorial papers included in this volume together with four invited talks were carefully reviewed and selected from 28 submissions. The papers are organized in the following topical sections: reversible concurrent computation; quantum circuits; reversible programming languages; and applications.
Book Synopsis Reversible Computation by : Alexis De Vos
Download or read book Reversible Computation written by Alexis De Vos and published by Springer. This book was released on 2012-04-13 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Reversible Computation, RC 2011, held in Gent, Belgium, in July 2011. The 10 revised full papers presented were carefully reviewed and selected from 25 initial submissions for inclusion in the book. The papers are devoted to all aspects of reversible computation, ranging from theoretical and experimental aspects to various applications. Topics addressed are: functional language for reversible computations, logic design, reversible circuits designed by a software toolkit called RevKit, application of reversible computation to the domain of quantum circuits, and physical realizations of reversible circuits in CMOS technologies.
Book Synopsis Reversible Computation by : Shigeru Yamashita
Download or read book Reversible Computation written by Shigeru Yamashita and published by Springer Nature. This book was released on 2021-06-22 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Reversible Computation, RC 2021, which was held online during July 7-8, 2021. The 11 papers included in this book were carefully reviewed and selected from 21 submissions. The book also contains 2 invited talks in full-paper length, 3 work-in-progress papers and 1 tool paper. They were organized in topical sections named: programming and programming languages; reversible concurrent computation; theory and foundations; and circuit synthesis.
Book Synopsis Methods for Efficient Synthesis of Large Reversible Binary and Ternary Quantum Circuits and Applications of Linear Nearest Neighbor Model by :
Download or read book Methods for Efficient Synthesis of Large Reversible Binary and Ternary Quantum Circuits and Applications of Linear Nearest Neighbor Model written by and published by . This book was released on 2013 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation describes the development of automated synthesis algorithms that construct reversible quantum circuits for reversible functions with large number of variables. Specifically, the research area is focused on reversible, permutative and fully specified binary and ternary specifications and the applicability of the resulting circuit to the physical limitations of existing quantum technologies. Automated synthesis of arbitrary reversible specifications is an NP hard, multiobjective optimization problem, where 1) the amount of time and computational resources required to synthesize the specification, 2) the number of primitive quantum gates in the resulting circuit (quantum cost), and 3) the number of ancillary qubits (variables added to hold intermediate calculations) are all minimized while 4) the number of variables is maximized. Some of the existing algorithms in the literature ignored objective 2 by focusing on the synthesis of a single solution without the addition of any ancillary qubits while others attempted to explore every possible solution in the search space in an effort to discover the optimal solution (i.e., sacrificed objective 1 and 4). Other algorithms resorted to adding a huge number of ancillary qubits (counter to objective 3) in an effort minimize the number of primitive gates (objective 2). In this dissertation, I first introduce the MMDSN algorithm that is capable of synthesizing binary specifications up to 30 variables, does not add any ancillary variables, produces better quantum cost (8-50% improvement) than algorithms which limit their search to a single solution and within a minimal amount of time compared to algorithms which perform exhaustive search (seconds vs. hours). The MMDSN algorithm introduces an innovative method of using the Hasse diagram to construct candidate solutions that are guaranteed to be valid and then selects the solution with the minimal quantum cost out of this subset. I then introduce the Covered Set Partitions (CSP) algorithm that expands the search space of valid candidate solutions and allows for exploring solutions outside the range of MMDSN. I show a method of subdividing the expansive search landscape into smaller partitions and demonstrate the benefit of focusing on partition sizes that are around half of the number of variables (15% to 25% improvements, over MMDSN, for functions less than 12 variables, and more than 1000% improvement for functions with 12 and 13 variables). For a function of n variables, the CSP algorithm, theoretically, requires n times more to synthesize; however, by focusing on the middle k (k by MMDSN which typically yields lower quantum cost. I also show that using a Tabu search for selecting the next set of candidate from the CSP subset results in discovering solutions with even lower quantum costs (up to 10% improvement over CSP with random selection). In Chapters 9 and 10 I question the predominant methods of measuring quantum cost and its applicability to physical implementation of quantum gates and circuits. I counter the prevailing literature by introducing a new standard for measuring the performance of quantum synthesis algorithms by enforcing the Linear Nearest Neighbor Model (LNNM) constraint, which is imposed by the today's leading implementations of quantum technology. In addition to enforcing physical constraints, the new LNNM quantum cost (LNNQC) allows for a level comparison amongst all methods of synthesis; specifically, methods which add a large number of ancillary variables to ones that add no additional variables. I show that, when LNNM is enforced, the quantum cost for methods that add a large number of ancillary qubits increases significantly (up to 1200%). I also extend the Hasse based method to the ternary and I demonstrate synthesis of specifications of up to 9 ternary variables (compared to 3 ternary variables that existed in the literature). I introduce the concept of ternary precedence order and its implication on the construction of the Hasse diagram and the construction of valid candidate solutions. I also provide a case study comparing the performance of ternary logic synthesis of large functions using both a CUDA graphic processor with 1024 cores and an Intel i7 processor with 8 cores. In the process of exploring large ternary functions I introduce, to the literature, eight families of ternary benchmark functions along with a Multiple Valued file specification (the Extended Quantum Specification XQS). I also introduce a new composite quantum gate, the multiple valued Swivel gate, which swaps the information of qubits around a centrally located pivot point. In summary, my research objectives are as follows: * Explore and create automated synthesis algorithms for reversible circuits both in binary and ternary logic for large number of variables. * Study the impact of enforcing Linear Nearest Neighbor Model (LNNM) constraint for every interaction between qubits for reversible binary specifications. * Advocate for a revised metric for measuring the cost of a quantum circuit in concordance with LNNM, where, on one hand, such a metric would provide a way for balanced comparison between the various flavors of algorithms, and on the other hand, represents a realistic cost of a quantum circuit with respect to an ion trap implementation. * Establish an open source repository for sharing the results, software code and publications with the scientific community. With the dwindling expectations for a new lifeline on silicon-based technologies, quantum computations have the potential of becoming the future workhorse of computations. Similar to the automated CAD tools of classical logic, my work lays the foundation for creating automated tools for constructing quantum circuits from reversible specifications.
Book Synopsis Algorithms and Theory of Computation Handbook, Volume 2 by : Mikhail J. Atallah
Download or read book Algorithms and Theory of Computation Handbook, Volume 2 written by Mikhail J. Atallah and published by CRC Press. This book was released on 2009-11-20 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook, Second Edition: Special Topics and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems.Along with updating and revising many of
Book Synopsis Computational Science – ICCS 2020 by : Valeria V. Krzhizhanovskaya
Download or read book Computational Science – ICCS 2020 written by Valeria V. Krzhizhanovskaya and published by Springer Nature. This book was released on 2020-06-18 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seven-volume set LNCS 12137, 12138, 12139, 12140, 12141, 12142, and 12143 constitutes the proceedings of the 20th International Conference on Computational Science, ICCS 2020, held in Amsterdam, The Netherlands, in June 2020.* The total of 101 papers and 248 workshop papers presented in this book set were carefully reviewed and selected from 719 submissions (230 submissions to the main track and 489 submissions to the workshops). The papers were organized in topical sections named: Part I: ICCS Main Track Part II: ICCS Main Track Part III: Track of Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Track of Agent-Based Simulations, Adaptive Algorithms and Solvers; Track of Applications of Computational Methods in Artificial Intelligence and Machine Learning; Track of Biomedical and Bioinformatics Challenges for Computer Science Part IV: Track of Classifier Learning from Difficult Data; Track of Complex Social Systems through the Lens of Computational Science; Track of Computational Health; Track of Computational Methods for Emerging Problems in (Dis-)Information Analysis Part V: Track of Computational Optimization, Modelling and Simulation; Track of Computational Science in IoT and Smart Systems; Track of Computer Graphics, Image Processing and Artificial Intelligence Part VI: Track of Data Driven Computational Sciences; Track of Machine Learning and Data Assimilation for Dynamical Systems; Track of Meshfree Methods in Computational Sciences; Track of Multiscale Modelling and Simulation; Track of Quantum Computing Workshop Part VII: Track of Simulations of Flow and Transport: Modeling, Algorithms and Computation; Track of Smart Systems: Bringing Together Computer Vision, Sensor Networks and Machine Learning; Track of Software Engineering for Computational Science; Track of Solving Problems with Uncertainties; Track of Teaching Computational Science; Track of UNcErtainty QUantIficatiOn for ComputationAl modeLs *The conference was canceled due to the COVID-19 pandemic.
Book Synopsis Reversible Logic Synthesis and Quantum Circuit Verification with Binary Decision Diagrams by : 魏駿宇
Download or read book Reversible Logic Synthesis and Quantum Circuit Verification with Binary Decision Diagrams written by 魏駿宇 and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Research and Applications in Global Supercomputing by : Segall, Richard S.
Download or read book Research and Applications in Global Supercomputing written by Segall, Richard S. and published by IGI Global. This book was released on 2015-01-31 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapidly generating and processing large amounts of data, supercomputers are currently at the leading edge of computing technologies. Supercomputers are employed in many different fields, establishing them as an integral part of the computational sciences. Research and Applications in Global Supercomputing investigates current and emerging research in the field, as well as the application of this technology to a variety of areas. Highlighting a broad range of concepts, this publication is a comprehensive reference source for professionals, researchers, students, and practitioners interested in the various topics pertaining to supercomputing and how this technology can be applied to solve problems in a multitude of disciplines.
