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Compact representations for the design of quantum logic

Author: Philipp Niemann; Robert Wille
Publisher: Cham, Switzerland : Springer, [2017]
Series: SpringerBriefs in physics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version :
(OCoLC)992781206
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Philipp Niemann; Robert Wille
ISBN: 9783319637242 331963724X
OCLC Number: 1021272920
Description: 1 online resource (viii, 125 pages) : 43 illustrations
Contents: Preface; Contents; Introduction and Background; 1 Introduction; 1.1 Quantum Mechanics and Quantum Logic; 1.2 Quantum Computation and Circuit Design; 1.3 Topics Covered in This Book; 2 Background; 2.1 Boolean Logic; 2.2 Quantum Logic; 2.2.1 Qubits and Measurement; 2.2.2 Quantum Operations; 2.3 Quantum Circuits and Gate Libraries; Representation of Quantum Functionality; 3 Challenges and Initial Approaches; 3.1 From Conventional to Quantum Logic; 3.2 Decision Diagrams for Quantum Logic; 3.2.1 Basic Concepts: Binary Decision Diagrams (BDDs); 3.2.2 Still Boolean: Quantum Decision Diagrams (QDDs). 3.2.3 Characteristic Functions: QuIDDs and XQDDs4 Quantum Multiple-Valued Decision Diagrams; 4.1 Basic Concepts; 4.2 Formal Definition; 4.3 Canonicity; 4.4 Construction and Manipulation; 4.4.1 Normalization; 4.4.2 Matrix Operations; 4.4.3 Construction; 4.5 Changing the Variable Order; 4.5.1 Shared Vertices and Skipped Variables; 4.5.2 Local Modifications and Vertex Weights; 4.5.3 Variable Interchange Scheme for QMDDs; 4.6 Efficiency of QMDDs; 5 Discussion and Outlook; Design of Quantum Logic; 6 Challenges and Initial Approaches; 6.1 Design Challenges; 6.2 Initial Synthesis Approaches. 6.2.1 Synthesis of Boolean Components6.2.2 Synthesis of Arbitrary Quantum Functionality; 7 Synthesis of Quantum Circuits; 7.1 Synthesis of Boolean Components; 7.1.1 Embedding: Handling Irreversible Function Descriptions; 7.1.2 Construction of QMDDs for Boolean Functions; 7.1.3 QMDD-Based Synthesis of Reversible Circuits; 7.2 Synthesis of Clifford Group Operations; 7.2.1 Main Concepts of the Synthesis Approach; 7.2.2 Algorithm; 7.2.3 Theoretical Analysis; 7.2.4 Experimental Results; 7.3 Conclusions; 8 Correctness of Multiple-Valued Implementations; 8.1 Multi-level Quantum Systems. 8.2 Equivalence Checking in Multi-level Quantum Systems8.2.1 Functional Equivalence for Quantum Operations; 8.2.2 Proposed Equivalence Checking Scheme; 8.2.3 Implementation Using QMDDs; 8.3 Experimental Results; 8.4 Conclusions; 9 Discussion and Outlook; References.
Series Title: SpringerBriefs in physics.
Responsibility: Philipp Niemann, Robert Wille.

Abstract:

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.  Read more...

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"This book is in the area of quantum computer design. It proposes a new approach for such designs. It provides the background information required to understand the new approach. It also describes Read more...

 
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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. 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