• Corpus ID: 220381076

Grover search with smaller oracles

  title={Grover search with smaller oracles},
  author={Dan Li},
  journal={arXiv: General Physics},
  • Dan Li
  • Published 6 July 2020
  • Computer Science
  • arXiv: General Physics
Grover search is one of the most important quantum algorithms. In this paper, we consider a kind of search that the conditions of satisfaction $T$ can be rewritten as $T=T_1\bigcap T_2$. Then we present a new Grover search with smaller oracles. The time complexity of this algorithm $O(\frac{\pi}{4}\sqrt{\frac{N}{b\lambda}}+\frac{\pi}{4}\sqrt{\frac{b}{\tau}})$, which is smaller than the time complexity of original Grover search, i.e. $O(\frac{\pi}{4}\sqrt{\frac{N}{M}})$. 

Figures from this paper


Simple Algorithm for Partial Quantum Search
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.
Is partial quantum search of a database any easier?
The lower bound for algorithms that return the correct answer with certainty is proved by reducing the usual database search problem to this partial search problem, and invoking Zalka's lower bound showing that Grovers algorithm is optimal for the usualdatabase search problem.
Quantum random-walk search algorithm
It will be shown that this algorithm performs an oracle search on a database of N items with $O(\sqrt{N})$ calls to the oracle, yielding a speedup similar to other quantum search algorithms.
A fast quantum mechanical algorithm for database search
In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) .
Quantum Mechanics Helps in Searching for a Needle in a Haystack
Quantum mechanics can speed up a range of search applications over unsorted data. For example, imagine a phone directory containing $N$ names arranged in completely random order. To find someone's
Quantum Partial Search of a Database with Several Target Items
This work presents a fast quantum algorithm, which finds one of the target blocks in an unstructured database separated into blocks of equal size, based on Boyer, Brassard, Hoyer, and Tapp algorithm and on Grover–Radhakrishnan algorithm of partial search.
Quantum partial search for uneven distribution of multiple target items
By perturbation method, this paper finds that the quantum partial search algorithm for multiple target items unevenly distributed in a database runs the fastest when target items are evenly distributed in database.
Depth optimization of quantum wasrch algorithms beyond Grover' algorithm2020