This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database can search a database for a unique item satisfying a given condition, in a single query [a query is defined as any question to the database to which the database has to return a (yes/no answer]. A classical algorithm will be limited to the information theoretic bound of at least
log2N queries, which it would achieve by using a binary search.
Sorting is a fundamental computational process that facilitates subsequent searching of a database. It can be thought of as factorization of the search process. The location of a desired item in a sorted database can be found by classical queries that inspect one letter of the label at a time. For an unsorted database, no such classical quick search algorithm is available. If the database permits quantum queries, however, then mere digitization is sufficient for efficient search. Sorting becomes redundant with the quantum superposition of states. A quantum algorithm is written down that locates the desired item in an unsorted database a factor of two faster than the best classical algorithm can in a sorted database. This algorithm has close resemblance to the assembly process in DNA replication.
A quantum mechanical computer can search a database consisting of N items in O(sqrt(N)) elementary quantum queries (a query is defined as any question to the database to which a binary (YES/NO) answer is required; an elementary query is a query pertaining to only one of the N possible states). A classical computer would take at least O(N) elementary queries. This paper shows that a quantum mechanical algorithm that can query information relating to multiple states, can search the database in a single query. A classical algorithm will be limited to the information theoretic bound of at least O(log N)queries (which it would achieve by using a binary search). A similar result was recently independently obtained by Terhal & Smolin by a different method.