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Reversible and Quantum Circuits: Optimization and Complexity Analysis 1st ed. 2016 [Kõva köide]

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  • Formaat: Hardback, 186 pages, kõrgus x laius: 235x155 mm, kaal: 553 g, 3 Illustrations, color; 102 Illustrations, black and white; XXII, 186 p. 105 illus., 3 illus. in color., 1 Hardback
  • Ilmumisaeg: 14-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319319353
  • ISBN-13: 9783319319353
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Reversible and Quantum Circuits: Optimization and Complexity Analysis 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 186 pages, kõrgus x laius: 235x155 mm, kaal: 553 g, 3 Illustrations, color; 102 Illustrations, black and white; XXII, 186 p. 105 illus., 3 illus. in color., 1 Hardback
  • Ilmumisaeg: 14-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319319353
  • ISBN-13: 9783319319353
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319319353.html
Märksõnad:

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.

1 Introduction
1(8)
1.1 Book Overview
4(2)
1.1.1 Optimization of Quantum Circuits
4(1)
1.1.2 Complexity Analysis
5(1)
1.2 Outline
6(3)
2 Background
9(36)
2.1 Boolean Functions
9(1)
2.2 Boolean Function Decomposition
10(3)
2.2.1 Ashenhurst Decomposition
10(1)
2.2.2 Curtis Decomposition
11(1)
2.2.3 Bi-decomposition
12(1)
2.2.4 Multiplexer Decomposition
12(1)
2.3 Exclusive-OR Sum of Products
13(2)
2.4 Boolean Satisfiability and SAT Modulo Theory
15(1)
2.5 Reversible Logic
16(7)
2.5.1 Reversible Function
17(3)
2.5.2 Reversible Gates
20(2)
2.5.3 Reversible Circuits
22(1)
2.6 Quantum Computation
23(8)
2.6.1 Quantum Systems
24(2)
2.6.2 Quantum Libraries
26(4)
2.6.3 Quantum Circuits
30(1)
2.7 Cost Metrics for Reversible and Quantum Circuits
31(5)
2.7.1 Quantum Cost
31(2)
2.7.2 Number of Gates
33(1)
2.7.3 Number of Lines
34(1)
2.7.4 Depth
35(1)
2.7.5 Nearest Neighbor Cost
36(1)
2.8 Decision Diagrams
36(9)
2.8.1 Binary Decision Diagrams
36(2)
2.8.2 Quantum Multiple-Valued Decision Diagrams
38(7)
3 Optimizations and Complexity Analysis on the Reversible Level
45(46)
3.1 Related Work
45(7)
3.1.1 Optimization Approaches of Reversible Circuits
46(5)
3.1.2 Complexity of Reversible Circuits
51(1)
3.2 Exact Quantum Cost Optimization
52(13)
3.2.1 General Idea
52(1)
3.2.2 Encoding Using SMT
53(6)
3.2.3 Experimental Results
59(6)
3.3 Heuristic Quantum Cost Optimization
65(18)
3.3.1 Simulated Annealing
66(1)
3.3.2 Rewriting Rules
67(1)
3.3.3 Algorithms
68(3)
3.3.4 Experimental Results
71(12)
3.4 Complexity Analysis of Reversible Circuits
83(6)
3.4.1 Complexity of Single-Target Circuits
83(1)
3.4.2 Complexity of MPMCT Circuits
84(1)
3.4.3 Upper Bounds for Single-Target Gates
85(2)
3.4.4 Upper Bounds for Reversible Circuits
87(2)
3.5 Summary
89(2)
4 Optimization and Complexity Analysis on the Mapping Level
91(50)
4.1 Related Work
91(9)
4.1.1 Mapping Approaches
92(8)
4.1.2 Complexity of NCT Circuits
100(1)
4.2 Improving the Mapping of Single-Target Gates
100(12)
4.2.1 Motivation
101(1)
4.2.2 Mapping of Single-Target Gates
101(3)
4.2.3 Experimental Evaluation
104(7)
4.2.4 Remarks and Observations
111(1)
4.3 Improving the Mapping of MPMCT Gates to Clifford + T Circuits
112(15)
4.3.1 Clifford + T Aware Reversible Circuit Mapping
112(1)
4.3.2 Proposed Mapping Approaches
113(1)
4.3.3 MPMCT Gates Mapping
114(8)
4.3.4 Experimental Results
122(5)
4.4 Complexity Analysis of NCT Circuits
127(13)
4.4.1 Upper Bounds for MPMCT Gates
128(1)
4.4.2 Upper Bounds for Single-Target Gates
129(9)
4.4.3 Upper Bounds for NCT Circuits
138(2)
4.5 Summary
140(1)
5 Optimizations and Complexity Analysis on the Quantum Level
141(34)
5.1 Related Work
141(4)
5.1.1 Optimization of Quantum Circuits
141(4)
5.1.2 Complexity of Quantum Circuits
145(1)
5.2 Depth Optimization for NCV Circuits
145(11)
5.2.1 General Idea
147(1)
5.2.2 Optimization Approaches
148(5)
5.2.3 Experimental Results
153(3)
5.3 NCV-Cost Optimization
156(7)
5.3.1 Proposed Idea
157(1)
5.3.2 Application
158(1)
5.3.3 Experimental Results
159(4)
5.4 Complexity Analysis of Quantum Circuits
163(11)
5.4.1 Complexity of NCV Quantum Circuits
163(6)
5.4.2 Complexity of Clifford + T Quantum Circuits
169(5)
5.5 Summary
174(1)
6 Conclusions
175
References
179
Nabila Abdessaied is a researcher at the German Research Center for Artificial Intelligence (DFKI) since 2013. She received the Diplôme d'Ingénieur in computer science from the University of sciences in Tunis, Tunisia, in 2007.  Then, she obtained her Master degree in computer science from the National Engineering School of Sousse, Tunisia, in 2009. In 2012, she joined the Institute of Computer Science of the University of Bremen where she received her Dr.-Ing. degree in computer science in 2015. Nabila Abdessaied is interested in the optimization of reversible and quantum circuits and studying their complexity. Furthermore, she is also working in the field of requirements engineering using NLP techniques.

 













Rolf Drechsler is head of Cyber-Physical Systems department at the German Research Center for Artificial Intelligence (DFKI) since 2011. Furthermore, he is a Full Professor at the Institute of Computer Science, University of Bremen, since 2001. Before, he worked for the Corporate Technology Department of Siemens AG, and was with the Institute of Computer Science, Albert-Ludwig University of Freiburg/Breisgau, Germany. Rolf Drechsler received the Diploma and Dr. Phil. Nat. degrees in computer science from the Goethe-University in Frankfurt/Main, Germany, in 1992 and, respectively,1995. Rolf Drechsler focusses in his research at DFKI and in the Group for Computer Architecture, which he is heading at the Institute of Computer Science of the University of Bremen, on the development and design of data structures and algorithms with an emphasis on circuit and system design.