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Efficient Implementation Of Quantum Circuit Simulation With Decision Diagrams
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Book Synopsis Efficient Implementation of Quantum Circuit Simulation with Decision Diagrams by : Stefan Hillmich
Download or read book Efficient Implementation of Quantum Circuit Simulation with Decision Diagrams written by Stefan Hillmich and published by Springer Nature. This book was released on 2023-09-27 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an easy-to-read introduction into quantum computing as well as classical simulation of quantum circuits. The authors showcase the enormous potential that can be unleashed when doing these simulations using decision diagrams—a data structure common in the design automation community but hardly used in quantum computing yet. In fact, the covered algorithms and methods are able to outperform previously proposed solutions on certain use cases and, hence, provide a complementary solution to established approaches. The award-winning methods are implemented and available as open-source under free licenses and can be easily integrated into existing frameworks such as IBM’s Qiskit or Atos’ QLM.
Book Synopsis Quantum Circuit Simulation by : George F. Viamontes
Download or read book Quantum Circuit Simulation written by George F. Viamontes and published by Springer Science & Business Media. This book was released on 2009-08-04 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Circuit Simulation covers the fundamentals of linear algebra and introduces basic concepts of quantum physics needed to understand quantum circuits and algorithms. It requires only basic familiarity with algebra, graph algorithms and computer engineering. After introducing necessary background, the authors describe key simulation techniques that have so far been scattered throughout the research literature in physics, computer science, and computer engineering. Quantum Circuit Simulation also illustrates the development of software for quantum simulation by example of the QuIDDPro package, which is freely available and can be used by students of quantum information as a "quantum calculator."
Book Synopsis Noise-Aware Quantum Circuit Simulation with Decision Diagrams by : Thomas Grurl
Download or read book Noise-Aware Quantum Circuit Simulation with Decision Diagrams written by Thomas Grurl and published by Springer. This book was released on 2024-10-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an easy-to-read introduction to quantum computing, as well the classical simulation of quantum circuits with common types of error effects. The authors showcase the enormous potential that can be unleashed when doing these simulations using decision diagrams–a data-structure common in the design automation community, often used in quantum computing design tasks. The algorithms and methods described can outperform previously proposed solutions in some cases, providing a complementary solution to established approaches. Finally, the necessity of noise-aware classical quantum circuit simulation is demonstrated through a practical use-case: the evaluation of quantum error correcting codes.
Book Synopsis Model Checking Software by : Georgiana Caltais
Download or read book Model Checking Software written by Georgiana Caltais and published by Springer Nature. This book was released on 2023-05-01 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 29th International Symposium on Model Checking Software, SPIN 2023, held in Paris, France, during April 26–27, 2023. The 9 full papers and 2 short papers included in this book were carefully reviewed and selected from 21 submissions. They were organized in topical sections as follows: binary decision diagrams, concurrency, testing, synthesis, explicit-state model checking.
Book Synopsis Efficient Quantum Circuit Simulation by : George F. Viamontes
Download or read book Efficient Quantum Circuit Simulation written by George F. Viamontes and published by . This book was released on 2006 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introducing Design Automation for Quantum Computing by : Alwin Zulehner
Download or read book Introducing Design Automation for Quantum Computing written by Alwin Zulehner and published by Springer Nature. This book was released on 2020-04-07 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers readers an easy introduction into quantum computing as well as into the design for corresponding devices. The authors cover several design tasks which are important for quantum computing and introduce corresponding solutions. A special feature of the book is that those tasks and solutions are explicitly discussed from a design automation perspective, i.e., utilizing clever algorithms and data structures which have been developed by the design automation community for conventional logic (i.e., for electronic devices and systems) and are now applied for this new technology. By this, relevant design tasks can be conducted in a much more efficient fashion than before – leading to improvements of several orders of magnitude (with respect to runtime and other design objectives). Describes the current state of the art for designing quantum circuits, for simulating them, and for mapping them to real hardware; Provides a first comprehensive introduction into design automation for quantum computing that tackles practically relevant tasks; Targets the quantum computing community as well as the design automation community, showing both perspectives to quantum computing, and what impressive improvements are possible when combining the knowledge of both communities.
Book Synopsis Design and Evaluation of High-performance Quantum Circuit Components by : Richard Ellis Rines
Download or read book Design and Evaluation of High-performance Quantum Circuit Components written by Richard Ellis Rines and published by . This book was released on 2019 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computers promise to extend the domain of the computable, performing calculations thought to be intractable on any classical device. Rapid experimental and technological progress suggests that this promise could soon be realized. However, these first quantum computers will inevitably be both small, faulty, and expensive, demanding implementations of quantum algorithms which are compact, fast, and error-resistant. As the complexity of realizable quantum computers accelerates toward the threshold of quantum supremacy, their capacity to demonstrate a meaningful quantum advantage when applied to real-world tasks depends on the high-performance design, implementation, and analysis of quantum circuits. The first half of the thesis is devoted to Shor's factoring algorithm, seeking to determine the most efficient quantum circuit implementation of a quantum modular multiplier. Three such implementations are introduced which outperform the best known exact reversible modular multiplier circuits for most practical problem sizes. Reformulated in the framework of quantum Fourier transform (QFT) based arithmetic, two of these circuits are further shown to reduce modular multiplication to a constant number of QFT-like circuits, which can then parallelized to a linear-depth circuit with just 2n + O(log n) qubits. Motivated by this deconstruction, the final result in this portion is an algorithm for a 'SIMD QFT' - demonstrating that the parallel QFT can be efficiently implemented on a topologically-limited distributed ion-trap architecture with just a single global shuttling instruction. The second half of this thesis focuses on quantum signal processing (QSP), specifically as applied to quantum Hamiltonian simulation. Hamiltonian simulation promises to be one of the first practical applications for which a near-term device could demonstrate an advantage over all classical systems. We use high-performance classical tools to construct, optimize, and simulate quantum circuits subject to realistic error models in order to empirically determine the maximum tolerable error rate for a meaningful Hamiltonian simulation experiment on a near-term quantum computer. By exploiting symmetry inherent to the QSP circuit, we demonstrate that their capacity for quantum simulation can be increased by at least two orders of magnitude if errors are systematic and unitary. This portion concludes with a thorough description of the classical simulation software used for the this analysis..
Book Synopsis Compact Representations for the Design of Quantum Logic by : Philipp Niemann
Download or read book Compact Representations for the Design of Quantum Logic written by Philipp Niemann and published by Springer. This book was released on 2017-08-21 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses modern approaches and challenges of computer-aided design (CAD) of quantum circuits with a view to providing compact representations of quantum functionality. Focusing on the issue of quantum functionality, it presents Quantum Multiple-Valued Decision Diagrams (QMDDs – a means of compactly and efficiently representing and manipulating quantum logic. For future quantum computers, going well beyond the size of present-day prototypes, the manual design of quantum circuits that realize a given (quantum) functionality on these devices is no longer an option. In order to keep up with the technological advances, methods need to be provided which, similar to the design and synthesis of conventional circuits, automatically generate a circuit description of the desired functionality. To this end, an efficient representation of the desired quantum functionality is of the essence. While straightforward representations are restricted due to their (exponentially) large matrix descriptions and other decision diagram-like structures for quantum logic suffer from not comprehensively supporting typical characteristics, QMDDs employ a decomposition scheme that more naturally models quantum systems. As a result, QMDDs explicitly support quantum-mechanical effects like phase shifts and are able to take more advantage of corresponding redundancies, thereby allowing a very compact representation of relevant quantum functionality composed of dozens of qubits. This provides the basis for the development of sophisticated design methods as shown for quantum circuit synthesis and verification.
Book Synopsis Reversible Computation: Extending Horizons of Computing by : Irek Ulidowski
Download or read book Reversible Computation: Extending Horizons of Computing written by Irek Ulidowski and published by Springer Nature. This book was released on 2020-05-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first.
Book Synopsis Design Automation of Quantum Computers by : Rasit O. Topaloglu
Download or read book Design Automation of Quantum Computers written by Rasit O. Topaloglu and published by Springer Nature. This book was released on 2022-12-09 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a comprehensive, state-of-the-art reference to the design automation aspects of quantum computers. Given roadmaps calling for quantum computers with 2000 qubits in a few years, readers will benefit from the practical implementation aspects covered in this book. The authors discuss real hardware to the extent possible. Provides an up-to-date, single-source reference to design automation aspects of quantum computers; Presentation is not just theoretical, but substantiated with real quantum hardware; Covers multi-faceted aspects of quantum computers, providing readers with valuable information, no matter the direction in which technology moves.
Book Synopsis On the Synthesis of Quantum Circuits for Diagonal Operators in Quantum Computation by : Jonathan M. Welch
Download or read book On the Synthesis of Quantum Circuits for Diagonal Operators in Quantum Computation written by Jonathan M. Welch and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Diagonal unitary operators are commonly found in many quantum algorithms. They find application as analytical potential operators for quantum simulation, as well as for complex oracles used in quantum searches. However, in order to implement a quantum algorithm on a given quantum device, each operator must be decomposed into a sequence of fault-tolerant, device-level instructions. In general, to implement an $n$-qubit diagonal unitary {\em exactly} on a quantum computer generally requires $2 {n+1}-3$ one- and two-qubit gates. However, for most practical implementations of diagonal unitaries, some degree of approximation will be necessary if the circuit is to be efficient. In this thesis we develop two complementary methods for the approximate synthesis of quantum circuits for diagonal unitaries. We show how to apply these techniques to real-space quantum simulation and show how efficient high fidelity quantum simulations can be implemented with low-depth quantum circuits.
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 Quantum simulation experiments with superconducting circuits by : Braumüller, Jochen
Download or read book Quantum simulation experiments with superconducting circuits written by Braumüller, Jochen and published by KIT Scientific Publishing. This book was released on 2018-06-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the universal quantum computer seems not in reach for the near future, this work focusses on analog quantum simulation of intriguing quantum models of light-matter interactions, with the goal of achieving a computational speed-up as compared to classical hardware. Existing building blocks of quantum hardware are used from superconducting circuits, that have proven to be a very suitable experimental platform for the implementation of model Hamiltonians at a high degree of controllability.
Book Synopsis Multiple-Valued Logic by : D. Michael Miller
Download or read book Multiple-Valued Logic written by D. Michael Miller and published by Springer Nature. This book was released on 2022-05-31 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Valued Logic: Concepts and Representations begins with a survey of the use ofmultiple-valued logic in several modern application areas including electronic design automation algorithms and circuit design. The mathematical basis and concepts of various algebras and systems of multiple valued logic are provided including comparisons among various systems and examples of their application. The book also provides an examination of alternative representations of multiple-valued logic suitable for implementation as data structures in automated computer applications. Decision diagram structures for multiple valued applications are described in detail with particular emphasis on the recently developed quantum multiple valued decision diagram. Table of Contents: Multiple Valued Logic Applications / MVL Concepts and Algebra / Functional Representations / Reversible andQuantum Circuits / Quantum Multiple-Valued Decision Diagrams / Summary / Bibliography
Book Synopsis Automated Technology for Verification and Analysis by : Étienne André
Download or read book Automated Technology for Verification and Analysis written by Étienne André and published by Springer Nature. This book was released on 2023-10-18 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 21st International Symposium on Automated Technology for Verification and Analysis, ATVA 2023, held in Singapore, in October 2023. The symposium intends to promote research in theoretical and practical aspects of automated analysis, verification and synthesis by providing a forum for interaction between regional and international research communities and industry in related areas. The 30 regular papers presented together with 7 tool papers were carefully reviewed and selected from 150 submissions.The papers are divided into the following topical sub-headings: Temporal logics, Data structures and heuristics, Verification of programs and hardware.
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 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.
