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a quantum search algorithm that runs quadratically faster than any equivalent classical algorithm

Grover’s algorithm is a quantum search algorithm that runs quadratically faster than any equivalent classical algorithm.

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a quantum algorithm that finds with high probability the unique input to a black box function that produces a particular output value, using just O(sqrt N) evaluations of the function, where N is the size of the function’s domain

Grover’s algorithm is a quantum algorithm that finds with high probability the unique input to a black box function that produces a particular output value, using just O(sqrt N) evaluations of the function, where N is the size of the function’s domain.

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a (quantum-)circuit-SAT solver

Grover's algorithm is a (quantum-)circuit-SAT solver.

A quantum computing method called Grover’s algorithm

A quantum computing method called Grover’s algorithm, however, speeds up the process, turning that 128-bit key into the quantum-computational equivalent of a 64-bit key.

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The most notorious quantum algorithm in this framework

The most notorious quantum algorithm in this framework is Grover's algorithm.

the best known speedup for symmetric encryption, and symmetric encryptionhas the effect of halving the key length

Grover's algorithm is the best known speedup for symmetric encryption, and symmetric encryptionhas the effect of halving the key length.

a quantum algorithm for searching in unstructured databases

Grover’s algorithm is a quantum algorithm for searching in unstructured databases.

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a quantum algorithm for searching 'black box' functions

Grover's Algorithm is a quantum algorithm for searching 'black box' functions and could be used to reduce the search space for things like symmetric ciphers and hashes by as much as half (quadratic speedup).

a probabilistic quantum algorithm ) that finds (with high probability

Grover's algorithm is a probabilistic quantum algorithm that finds (with high probability) the unique input to a black box function that produces a particular output value, using $$ O({\sqrt {N}})

$1$. $$|\psi\rangle

Given $f:\{0, \ldots, N-1\} \to \{0, 1\}$ such that $f(x) = 1$ for exactly one $x$ (say $\omega$), Grover's algorithm amplifies the quantum state corresponding to $\omega$. Amplitude amplification is the generalized version that can amplify the quantum states corresponding to multiple entries, given their output is $1$. $$|\psi\rangle