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).[1]
  2. Grover's algorithm, which takes O(N1/2) time, is the fastest possible quantum algorithm for searching an unsorted database.[1]
  3. Like all quantum computer algorithms, Grover's algorithm is probabilistic, in the sense that it gives the correct answer with high probability.[1]
  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".[1]
  5. This is faster than the O ( N ) {\displaystyle O({\sqrt {N}})} steps taken by Grover's algorithm.[2]
  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.[2]
  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.[2]
  8. Grover's algorithm has implications for the security of symmetric-key cryptography as it can be used to search the key space.[2]
  9. Grover's algorithm searches a list of unstructured data for specific items.[3]
  10. You can build Grover's search algorithm with just a few lines of code.[3]
  11. What does Grover's search algorithm do?[3]
  12. Grover's algorithm asks whether an item in a list is the one we are searching for.[3]
  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.[4]
  14. Grover's algorithm searches a function for a single satisfying input.[5]
  15. So, if Grover's algorithm searches a function, how is that function represented?[5]
  16. However, since Grover's algorithm is almost entirely made up of Hadamard gates, I won't be covering them here.[5]
  17. We now return to Grover's algorithm.[5]
  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.[6]
  19. Grover's algorithm requires only O ( N ) \mathcal{O}(\sqrt{N}) O(N ​) evaluations of the Oracle.[7]
  20. Other examples where Grover's algorithm or similar methods are used are for instance minimization problems.[7]
  21. For comparison, we implemented the same approach for the 2 and 3 Grover's algorithms.[8]
  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.[9]
  23. However, implementing Grover's algorithm on a quantum system has been challenging.[9]
  24. Now in a new study, researchers have implemented Grover's algorithm with trapped atomic ions.[9]
  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.[9]
  26. Grover's search algorithm is designed to be executed on a quantum-mechanical computer.[10]
  27. In this article, the probabilistic wp-calculus is used to model and reason about Grover's algorithm.[10]

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