### Automatically assigned DDC number: 0041Manually assigned DDC number: 0040151

Number of references: 8

Title: A Fast Quantum Mechanical Algorithm for Database Search

Subject: A Fast Quantum Mechanical Algorithm for Database Search

Description: ed Problem Let a system have N = 2 n states which are labelled S 1 ,S 2 ,...S N . These 2 n states are represented as n bit strings. Let there be a unique state, say S n , that satisfies the condition C(S n ) = 1, whereas for all other states S, C(S) = 0 (assume that for any state S, the condition C(S) can be evaluated in unit time). The problem is to identify the state S n . 3. Algorithm (i) Initialize the system to the distribution: , i.e. there is the same amplitude to be in each of the N states. This distribution can be obtained in steps, as discussed in section 1.2. (ii) Repeat the following unitary operations times (the precise number of repetitions is important as discussed in [BBHT96]): (a) Let the system be in any state S: In case , rotate the phase by radians; In case , leave the system unaltered. (b) Apply the diffusion transform D which is defined by the matrix D as follows: if & . This diffusion transform, D, can be implemented as , where R the rotation matrix & W t...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1998-10-23

Pubyear: 1996

Format: ps

Identifier: http://citeseer.ist.psu.edu/175549.html

Source: http://infidel.c.u-tokyo.ac.jp/~ysato/seminar/grover.ps.gz

Language: en

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Rights: unrestricted

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