Simple Algorithm for Partial Quantum Search
Abstract
Quite often in database search, we only need to extract portion of the information about the satisfying item. Recently Radhakrishnan & Grover [RG] considered this problem in the following form: the database of $N$ items was divided into $K$ equally sized blocks. The algorithm has just to find the block containing the item of interest. The queries are exactly the same as in the standard database search problem. [RG] invented a quantum algorithm for this problem of partial search that took about $0.33\sqrt{N/K}$ fewer iterations than the quantum search algorithm. They also proved that the best any quantum algorithm could do would be to save $0.78 \sqrt(N/K)$ iterations. The main limitation of the algorithm was that it involved complicated analysis as a result of which it has been inaccessible to most of the community. This paper gives a simple analysis of the algorithm. This analysis is based on three elementary observations about quantum search, does not require a single equation and takes less than 2 pages.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2005
- DOI:
- 10.48550/arXiv.quant-ph/0504157
- arXiv:
- arXiv:quant-ph/0504157
- Bibcode:
- 2005quant.ph..4157K
- Keywords:
-
- Quantum Physics
- E-Print:
- 3 pages, 3 figures