Grover's algorithm

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1. Grover's algorithm is a quantum algorithm for searching an unsorted database with N entries in O(N1/2) time and using O(logN) storage space (see big O notation).
2. Grover's algorithm, which takes O(N1/2) time, is the fastest possible quantum algorithm for searching an unsorted database.
3. Like all quantum computer algorithms, Grover's algorithm is probabilistic, in the sense that it gives the correct answer with high probability.
4. Although the purpose of Grover's algorithm is usually described as "searching a database", it may be more accurate to describe it as "inverting a function".
5. This is faster than the O ( N ) {\displaystyle O({\sqrt {N}})} steps taken by Grover's algorithm.
6. Grover's algorithm could brute-force a 128-bit symmetric cryptographic key in roughly 264 iterations, or a 256-bit key in roughly 2128 iterations.
7. Like many quantum algorithms, Grover's algorithm is probabilistic in the sense that it gives the correct answer with a probability of less than 1.
8. Grover's algorithm has implications for the security of symmetric-key cryptography as it can be used to search the key space.
9. Grover's algorithm searches a list of unstructured data for specific items.
10. You can build Grover's search algorithm with just a few lines of code.
11. What does Grover's search algorithm do?
12. Grover's algorithm asks whether an item in a list is the one we are searching for.
13. To clear the role coherence plays on the essential operator level in Grover's search algorithm, here we discuss the coherence dynamics of the state after each basic operator is applyied.
14. Grover's algorithm searches a function for a single satisfying input.
15. So, if Grover's algorithm searches a function, how is that function represented?
16. However, since Grover's algorithm is almost entirely made up of Hadamard gates, I won't be covering them here.
17. We now return to Grover's algorithm.
18. Essentially, Grover's algorithm applies when you have a function which returns True for one of its possible inputs, and False for all the others.
19. Grover's algorithm requires only O ( N ) \mathcal{O}(\sqrt{N}) O(N ​) evaluations of the Oracle.
20. Other examples where Grover's algorithm or similar methods are used are for instance minimization problems.
21. For comparison, we implemented the same approach for the 2 and 3 Grover's algorithms.
22. Previous research has shown that Grover's search algorithm, proposed in 1996, is an optimal quantum search algorithm, meaning no other quantum algorithm can search faster.
23. However, implementing Grover's algorithm on a quantum system has been challenging.
24. Now in a new study, researchers have implemented Grover's algorithm with trapped atomic ions.
25. Grover's algorithm, on the other hand, first initializes the system in a quantum superposition of all 8 states, and then uses a quantum function called an oracle to mark the correct solution.
26. Grover's search algorithm is designed to be executed on a quantum-mechanical computer.
27. In this article, the probabilistic wp-calculus is used to model and reason about Grover's algorithm.

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