Perturbation Theory for Solid-state Quantum Computation with Many Quantum Bits

Download or read book Perturbation Theory for Solid-state Quantum Computation with Many Quantum Bits written by Gennady P. Berman and published by Rinton PressInc. This book was released on 2005 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quantum computer is expected capable to solve a vast range of mathematical and physical problems much faster than a classical computer. In order to be useful, the register of a quantum computer must contain a large number of qubits. Numerical simulations of quantum dynamics of a many-qubit quantum computer (for optimization of parameters, benchmarking, and architecture design) requires diagonalization of exponentially large matrices or integration for a long time of an exponentially large system of coupled differential equations. In this book, a theoretical approach is presented, wich solves the above problem by using a quantum-mechanical perturbation theory. The perturbation theory is based on small parameters that naturally appear in the system. The results of numerical simulations are widely used to support the theoretical propositions. It is demonstrated how to simulate simple quantum logic operations and quantum protocols involving a large number of qubits (up to 2000). It is especially useful for minimizing the effects of most types of errors encountered in solid-state quantum computers. Implementations of quantum algorithms are demonstrated in spin systems, quantum dots, and superconducting systems. Almost all results of the book are derived from the first principles. This book is useful for scientists, engineers, and students who are interested in quantum computing.