Quantum Circuit Simulation

1 Introduction. 1.1 Quantum Circuits. 1.2 Quantum Simulation. 1.3 Book. 2 Gate Modeling and Circuit Simulation. 2.1 Classical Digital Circuits. 2.2 Simulation with Binary Decision Diagrams. 2.3 Sequential Circuits and Synchronization. 2.4 Summary. 3 Linear Algebra and Quantum Mechanics. 3.1 Linear Algebra. 3.2 Quantum Mechanics. 3.3 Summary. 4 Quantum Information Processing. 4.1 Quantum Gates. 4.2 Quantum Circuits. 4.3 Synchronization of Quantum Circuits. 4.4 Sample Algorithms. 4.5 Summary. 5 Special Case: Simulating Stabilizer Circuits. 5.1 Basics of a Quantum Circuit Simulator. 5.2 Stabilizer States, Gates and Circuits. 5.3 Data structures. 5.4 Algorithms. 5.5 Summary. 6 Generic Circuit Simulation Techniques. 6.1 Qubit-wise Multiplication. 6.2 P-blocked Simulation. 6.3 Tensor Networks. 6.4 Slightly-entangled Simulation. 6.5 Summary. 7 State-Vector Simulation with Decision Diagrams. 7.1 Quantum Information Decision Diagrams. 7.2 Scalability of QuIDD-based Simulation. 7.3 Empirical Validation. 7.4 Related Decision Diagrams. 7.5 Summary. 8 Density-Matrix Simulation with QuIDDs. 8.1 QuIDD Properties and Density Matrices. 8.2 QuIDD-based Outer Product. 8.3 QuIDD-based Partial Trace. 8.4 Empirical Validation. 8.5 Summary. 9 Checking Equivalence of States and Circuits. 9.1 Quantum Equivalence Checking. 9.2 Global-Phase Equivalence. 9.3 Relative-Phase Equivalence. 9.4 Empirical Validation. 9.5 Summary. 10 Improving QuIDD-based Simulation. 10.1 Gate Algorithms. 10.2 Dynamic Tensor Products and Partial Tracing. 10.3 Empirical Validation. 10.4 Summary. 11 Closing Remarks. A QuIDDPro Simulator. A.1 Running the Simulator. A.2 Functions and Code in Multiple Files. A.3 Language Reference. B QuIDDPro Examples. B.1 Well-known Quantum States. B.2 Grover's Search Algorithm. B.3 Shor's Integer Factoring Algorithm. References. Index.