: George F. Viamontes, Igor L. Markov, John P. Hayes
: Quantum Circuit Simulation
: Springer-Verlag
: 9789048130658
: 1
: CHF 85.20
:
: Elektronik, Elektrotechnik, Nachrichtentechnik
: English
: 190
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Qu ntum 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.

Preface4
Contents7
1 Introduction9
1.1 Quantum Circuits9
1.2 Quantum Simulation11
1.3 Book Outline12
Acknowledgments13
2 Gate Modeling and Circuit Simulation14
2.1 Classical Digital Circuits14
2.2 Simulation with Binary Decision Diagrams18
2.3 Sequential Circuits and Synchronization24
2.4 Summary25
3 Linear Algebra and Quantum Mechanics26
3.1 Linear Algebra26
3.2 Quantum Mechanics31
3.3 Summary39
4 Quantum Information Processing40
4.1 Quantum Gates40
4.2 Quantum Circuits45
4.3 Synchronization of Quantum Circuits49
4.4 Sample Algorithms50
4.5 Summary53
5 Special Case: Simulating Stabilizer Circuits54
5.1 Basics of a Quantum Circuit Simulator54
5.2 Stabilizer States, Gates and Circuits56
5.3 Data Structures58
5.4 Algorithms59
5.5 Summary62
6 Generic Circuit Simulation Techniques65
6.1 Qubit-wise Multiplication65
6.2 P-blocked Simulation67
6.3 Tensor Networks69
6.4 Slightly-entangled Simulation72
6.5 Summary76
7 State-Vector Simulation with Decision Diagrams77
7.1 Quantum Information Decision Diagrams77
7.2 Scalability of QuIDD-based Simulation86
7.3 Empirical Validation94
7.4 Related Decision Diagrams98
7.5 Summary106
8 Density-Matrix Simulation with QuIDDs108
8.1 QuIDD Properties and Density Matrices108
8.2 QuIDD-based Outer Product110
8.3 QuIDD-based Partial Trace111
8.4 Empirical Validation114
8.5 Summary119
9 Checking Equivalence of States and Circuits120
9.1 Quantum Equivalence Checking120
9.2 Global-Phase Equivalence122
9.3 Relative-Phase Equivalence127
9.4 Empirical Validation131
9.5 Summary133
10 Improving QuIDD-based Simulation137
10.1 Gate Algorithms137
10.2 Dynamic Tensor Products and Partial Tracing143
10.3 Empirical Validation149
10.4 Summary154
11 Closing Remarks157
Appendix A QuIDDPro Simulator159
A.1 Running the Simulator159
A.2 Functions and Code in Multiple Files162
A.3 Language Reference164
Appendix B QuIDDPro Examples180
B.1 Well-known Quantum States180
B.2 Grover’s Search Algorithm181
B.3 Shor’s Integer Factoring Algorithm182
References184
Index190