Viamontes G.F., Markov I.L., Hayes J.P. Quantum Circuit Simulation

New York: Springer, 2009. — 194 p.The construction of computer algorithms and software models that simulatephysical systems plays a fundamental role in all branches of science and engineering.The physicist and Nobel laureate Richard Feynman, among others,observed in the 1980s that the important task of simulating quantummechanicalprocesses on a standard computer requires an extraordinaryamount of computer memory and runtime. Such observations gave rise tothe notion of quantum computing, where quantum mechanics itself is used tosimulate quantum behavior. The key insight is to replace the familiar 0 and 1 bits of conventional or classical computing with information units calledqubits (quantum bits) that capture quantum states of elementary particles oratomic nuclei. By operating on qubits, a quantum computer can, in principle,process exponentially more data than a classical computer in a similar numberof steps. In the 1990s, several fast quantum methods were discovered for suchapplications as searching large databases and factoring large numbers; the latter is a basic step in some forms of codebreaking.Quantum Circuits.
Quantum Simulation.
Book Outline.
Gate Modeling and Circuit Simulation.
Classical Digital Circuits.
Simulation with Binary Decision Diagrams.
Sequential Circuits and Synchronization.
Summary.
Linear Algebra and Quantum Mechanics.
Linear Algebra.
Quantum Mechanics.
Summary.
Quantum Information Processing.
Quantum Gates.
Quantum Circuits.
Synchronization of Quantum Circuits.
Sample Algorithms.
Summary.
Special Case: Simulating Stabilizer Circuits.
Basics of a Quantum Circuit Simulator.
Stabilizer States, Gates and Circuits.
Data structures.
Algorithms.
Summary.
Generic Circuit Simulation Techniques.
Qubit-wise Multiplication.
P-blocked Simulation.
Tensor Networks.
Slightly-entangled Simulation.
Summary.
State-Vector Simulation with Decision.
Quantum Information Decision Diagrams.
Scalability of QuIDD-based Simulation.
Empirical Validation.
Related Decision Diagrams.
Summary.
Density-Matrix Simulation with QuIDDs.
QuIDD Properties and Density Matrices.
QuIDD-based Outer Product.
QuIDD-based Partial Trace.
Empirical Validation.
Summary.
Checking Equivalence of States and Circuits.
Quantum Equivalence Checking.
Global-Phase Equivalence.
Relative-Phase Equivalence.
Empirical Validation.
Summary.
Improving QuIDD-based Simulation.
Closing Remarks.
QuIDDPro Simulator.
QuIDDPro Examples.