Quantum Circuit Simulation

✍ Scribed by George F. Viamontes, Igor L. Markov, John P. Hayes

• Publisher: Springer
• Year: 2009
• Tongue: English
• Leaves: 194
• Edition: 1
• Category: Library

✦ Synopsis

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."

✦ Table of Contents

Cover Page......Page 1
Quantum Circuit Simulation......Page 3
ISBN 9789048130641......Page 4
Preface......Page 5
Contents......Page 8
1.1 Quantum Circuits......Page 10
1.2 Quantum Simulation......Page 12
1.3 Book Outline......Page 13
Acknowledgments......Page 14
2.1 Classical Digital Circuits......Page 15
2.2 Simulation with Binary Decision Diagrams......Page 19
2.3 Sequential Circuits and Synchronization......Page 25
2.4 Summary......Page 26
3.1 Linear Algebra......Page 27
3.2 Quantum Mechanics......Page 32
3.3 Summary......Page 40
4.1 Quantum Gates......Page 41
4.2 Quantum Circuits......Page 46
4.3 Synchronization of Quantum Circuits......Page 50
4.4 Sample Algorithms......Page 51
4.5 Summary......Page 54
5.1 Basics of a Quantum Circuit Simulator......Page 55
5.2 Stabilizer States, Gates and Circuits......Page 57
5.3 Data structures......Page 59
5.4 Algorithms......Page 60
5.5 Summary......Page 63
6.1 Qubit-wise Multiplication......Page 66
6.2 P-blocked Simulation......Page 68
6.3 Tensor Networks......Page 70
6.4 Slightly-entangled Simulation......Page 73
6.5 Summary......Page 77
7.1 Quantum Information Decision Diagrams......Page 78
7.2 Scalability of QuIDD-based Simulation......Page 87
8.1 QuIDD Properties and Density Matrices......Page 109
8.2 QuIDD-based Outer Product......Page 111
8.3 QuIDD-based Partial Trace......Page 112
8.4 Empirical Validation......Page 115
8.5 Summary......Page 120
9.1 Quantum Equivalence Checking......Page 121
9.2 Global-Phase Equivalence......Page 123
9.3 Relative-Phase Equivalence......Page 128
9.4 Empirical Validation......Page 132
9.5 Summary......Page 134
10.1 Gate Algorithms......Page 138
10.2 Dynamic Tensor Products and Partial Tracing......Page 144
10.3 Empirical Validation......Page 150
11 Closing Remarks......Page 158
A.1 Running the Simulator......Page 160
A.2 Functions and Code in Multiple Files......Page 163
A.3 Language Reference......Page 165
B.1 Well-known Quantum States......Page 181
B.2 Grover’s Search Algorithm......Page 182
B.3 Shor’s Integer Factoring Algorithm......Page 183
References......Page 185
Index......Page 191