Some researchers suggest achieving massive speedups in computing by exploiting quantum-mechanical effects such as superposition (quantum parallelism) and entanglement.1 A quantum algorithm typically consists of applying quantum gates to quantum states, but because the input to the algorithm might be normal classical bits (or nonquantum), it affects only the selection of quantum gates. After all...

Searching an item in an unsorted database with size N costs a classical computer O(N) running time. Can a quantum computer search a needle in a haystack much more efficient than its classical counterpart? Grover, in 1996, affirmatively answered this question by proposing a search algorithm [4], which consults the database only O( N ) times. In contrast to algorithms based on the quantum Fourier...

Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately π/4 √ N queries to a quantum oracle. For classical search using a classical oracle, the search complexity is of order N/2 queries since on average half of the items must be searched. In work preceding Grover’s, Bennett et al. had shown that no quantum algorithm c...

One of computer science’s classic problems is that of the search. This paper will look at Lou K. Grover’s Quantum Search algorithm. This algorithm is used to search a database, or search space, that is not, and cannot be, sorted or structured. It can produce a quadratic speed up over any similar classical search. This paper will also look at some of the issues and advances that have come out of...

A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to the underlying structure of abstract search spaces. The algorithm is evaluated empirically with a variety of search problems, and shown to be particularly ef...

We consider the problem of finding one or more desired items out of an unsorted database. Patel has shown that if the database permits quantum queries, then mere digitization is sufficient for efficient search for one desired item. The algorithm, called factorized quantum search algorithm, presented by him can locate the desired item in an unsorted database using O(log4N) queries to factorized ...