Compact representations for the design of quantum logic. ([2017])

• Record Type: Book
• Further Information: Note: Philipp Niemann, Robert Wille.
• Authors: Niemann, Philipp; Wille, Robert
• 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource (viii, 125 pages), 43 illustrations
• Subjects: 621.3; Physics; Quantum computing; Quantum logic; Quantum theory; Spintronics; Algebra -- Data processing; COMPUTERS -- General; Spintronics; Quantum theory; Quantum computing; Quantum logic; Computers -- Data Processing; Science -- Quantum Theory; Maths for computer scientists; Mathematical theory of computation; Quantum physics (quantum mechanics & quantum field theory); Computers -- Information Technology; Physics; Quantum Information Technology, Spintronics; Symbolic and Algebraic Manipulation; Quantum Computing; Quantum Physics; Electronic books
• Languages: English
• ISBNs: 9783319637242
• Related ISBNs: 331963724X; 9783319637235; 3319637231
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.