Viamontes / Markov / Hayes Quantum Circuit Simulation

1. Auflage 2009
ISBN: 978-90-481-3065-8
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 190 Seiten

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.'

George Viamontes has a Ph.D. in Computer Science and Enginering from the University of Michigan where his research was focused on quantum circuit simulation.  Through a Department of Energy fellowship for high-performance computer science, he completed a portion of his graduate research at Los Alamos National Laboratory.  Upon graduation, Dr. Viamontes spent a year at Lockheed Martin Advanced Technology Laboratories where he continued to work on quantum circuit simulation.  Currently he develops and implements algorithms for high-frequency automated trading and continues to consult for Lockheed Martin on quantum computing projects.Igor L. Markov is an associate professor of Electrical Engineering and Computer Science at the University of Michigan. He received his Ph.D. in Computer Science from UCLA. Currently he is a member of the Executive Board of ACM SIGDA, Editorial Board member of Communications of ACM, ACM TODAES, IEEE Transactions on Computers, IEEE Transactions on CAD, as well as IEEE Design & Test. Prof. Markov researches computers that make computers. He has co-authored two books and more than 160 refereed publications, some of which were honored by the best-paper awards at the Design Automation and Test in Europe Conference (DATE), the Int'l Symposium on Physical Design (ISPD) and IEEE Trans. on Computer-Aided Design. Prof. Markov is the recipient of a DAC Fellowship, an ACM SIGDA Outstanding New Faculty award, an NSF CAREER award, an IBM Partnership Award, and a Microsoft A. Richard Newton Breakthrough Research Award. John P. Hayes received the B.E. degree from the National University of Ireland, Dublin, and the M.S. and Ph.D. degrees from the University of Illinois, Urbana-Champaign, all in electrical engineering. While at the University of Illinois, he participated in the design of the ILLIAC III computer. In 1970 he joined the Operations Research Group at the Shell Benelux Computing Center in The Hague, where he worked on mathematical programming and software development. From 1972 to 1982 he was a faculty member of the Departments of Electrical Engineering-Systems and Computer Science of the University of Southern California, Los Angeles. Since 1982 he has been with the Electrical Engineering and Computer Science Department of the University of Michigan, Ann Arbor, where he holds the Claude E. Shannon Endowed Chair in Engineering Science.

Autoren/Hrsg.

Viamontes, George F.

Markov, Igor L.

Hayes, John P.

Inhaltsverzeichnis

1;Preface;4
2;Contents;7
3;1 Introduction;9
3.1;1.1 Quantum Circuits;9
3.2;1.2 Quantum Simulation;11
3.3;1.3 Book Outline;12
3.4;Acknowledgments;13
4;2 Gate Modeling and Circuit Simulation;14
4.1;2.1 Classical Digital Circuits;14
4.2;2.2 Simulation with Binary Decision Diagrams;18
4.3;2.3 Sequential Circuits and Synchronization;24
4.4;2.4 Summary;25
5;3 Linear Algebra and Quantum Mechanics;26
5.1;3.1 Linear Algebra;26
5.2;3.2 Quantum Mechanics;31
5.3;3.3 Summary;39
6;4 Quantum Information Processing;40
6.1;4.1 Quantum Gates;40
6.2;4.2 Quantum Circuits;45
6.3;4.3 Synchronization of Quantum Circuits;49
6.4;4.4 Sample Algorithms;50
6.5;4.5 Summary;53
7;5 Special Case: Simulating Stabilizer Circuits;54
7.1;5.1 Basics of a Quantum Circuit Simulator;54
7.2;5.2 Stabilizer States, Gates and Circuits;56
7.3;5.3 Data Structures;58
7.4;5.4 Algorithms;59
7.5;5.5 Summary;62
8;6 Generic Circuit Simulation Techniques;65
8.1;6.1 Qubit-wise Multiplication;65
8.2;6.2 P-blocked Simulation;67
8.3;6.3 Tensor Networks;69
8.4;6.4 Slightly-entangled Simulation;72
8.5;6.5 Summary;76
9;7 State-Vector Simulation with Decision Diagrams;77
9.1;7.1 Quantum Information Decision Diagrams;77
9.2;7.2 Scalability of QuIDD-based Simulation;86
9.3;7.3 Empirical Validation;94
9.4;7.4 Related Decision Diagrams;98
9.5;7.5 Summary;106
10;8 Density-Matrix Simulation with QuIDDs;108
10.1;8.1 QuIDD Properties and Density Matrices;108
10.2;8.2 QuIDD-based Outer Product;110
10.3;8.3 QuIDD-based Partial Trace;111
10.4;8.4 Empirical Validation;114
10.5;8.5 Summary;119
11;9 Checking Equivalence of States and Circuits;120
11.1;9.1 Quantum Equivalence Checking;120
11.2;9.2 Global-Phase Equivalence;122
11.3;9.3 Relative-Phase Equivalence;127
11.4;9.4 Empirical Validation;131
11.5;9.5 Summary;133
12;10 Improving QuIDD-based Simulation;137
12.1;10.1 Gate Algorithms;137
12.2;10.2 Dynamic Tensor Products and Partial Tracing;143
12.3;10.3 Empirical Validation;149
12.4;10.4 Summary;154
13;11 Closing Remarks;157
14;Appendix A QuIDDPro Simulator;159
14.1;A.1 Running the Simulator;159
14.2;A.2 Functions and Code in Multiple Files;162
14.3;A.3 Language Reference;164
15;Appendix B QuIDDPro Examples;180
15.1;B.1 Well-known Quantum States;180
15.2;B.2 Grover’s Search Algorithm;181
15.3;B.3 Shor’s Integer Factoring Algorithm;182
16;References;184
17;Index;190