Quantum computing and quantum search algorithms

Quantum computation is a field at the junction of modern quantum physics and theoretical computer science. It belongs to the class of the most innovative and revolutionary computing in the sense that fundamentally new devices and architectures need to be developed/designed, so need the very underlying Church-Miring principles to be adapted correspondingly, according to quantum mechanics. A brief introduction to quantum computing will be given in this dissertation. The existing quantum search algorithm of L. K. Grover finds a single search target in a large database with N items in O(N1/2) steps. The speedup is quadratic. We will extend the original Grover's search algorithm to multi-object search problems with the availability of partial information. We will also discuss several exact quantum search algorithms based on Grover's algorithm. Especially we will present a new algorithm which requires logarithmically many unitary iterations, carried out dynamically utilizing varying auxiliary functions. In addition, we will show how to design a quantum circuit for implementing Grover's algorithm.