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