# Is partial quantum search of a database any easier?

@inproceedings{Grover2004IsPQ,
title={Is partial quantum search of a database any easier?},
author={Lov K. Grover and Jaikumar Radhakrishnan},
booktitle={ACM Symposium on Parallelism in Algorithms and Architectures},
year={2004}
}
• Published in
ACM Symposium on Parallelism…
15 July 2004
• Computer Science
We consider the partial database search problem where given a quantum database <i>f</i> : {0,1}<sup>n</sup>→{0,1} such that <i>f</i>(<i>x</i>) =1 for a unique <i>x</i> ∈ {0,1}<sup>n</sup>, we are required to determine <i>only</i> the first <i>k</i> bits of the address <i>x</i>. We present an algorithm and derive a lower bound for this problem. Let <i>q</i>(<i>k,n</i>) be the minimum number of queries needed to find the first <i>k</i> bits of the required address <i>x</i> with certainty (or with…

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## References

SHOWING 1-9 OF 9 REFERENCES

• Computer Science
Quantum Inf. Process.
• 2006
A quantum algorithm is presented for this problem of partial search that takes about 0.34 $$\sqrt{b}$$ fewer iterations than the quantum search algorithm.
An infinite family of sure-success quantum algorithms are introduced here to solve Grover's search problem, each member for a different range of f, and are particularly useful when the cost of failure of a search is very high, and for multistage searches with a different search criterion for each stage.
• Computer Science
• 1996
A lower bound on the efficiency of any possible quantum database searching algorithm is provided and it is shown that Grover''s algorithm nearly comes within a factor 2 of being optimal in terms of the number of probes required in the table.
I show that for any number of oracle lookups up to about {pi}/4thinsp{radical} (N) , Grover{close_quote}s quantum searching algorithm gives the maximal possible probability of finding the desired
In a standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this paper we present a modified version of Grover's algorithm that searches a
• Physics, Computer Science
• 2000
This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
• Mathematics
• 2000
Consider a Boolean function $\chi: X \to \{0,1\}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $\chi(x)=1$ and bad otherwise. Consider also a quantum algorithm
• Computer Science
SIAM J. Comput.
• 1997
It is proved that relative to an oracle chosen uniformly at random with probability 1 the class $\NP$ cannot be solved on a quantum Turing machine (QTM) in time $o(2^{n/2})$.
For every prescribed success probability I give an algorithm consisting of several runs of Grover's algorithm that matches a recent bound by Buhrman and de Wolf on the order of the number of queries to the black box.