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Questions tagged [grovers-algorithm]

Grover's search algorithm is an algorithm that can perform a search in the order of square root of the input size. This is a provable speed up over the best classical algorithm, which requires a time of order N to perform a search.

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What applications does Grover's Search Algorithm have?

Grover's Search algorithm is usually talked about in terms of finding a marked entry in an unsorted database. This is a natural formalism that lets it be applied directly to searching for solutions to ...
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Grover's algorithm: where is the list?

Grover's algorithm is used, among other things, to search an item $\mathbf{y}$ in an unordered list of items $[\mathbf{x}_0, \mathbf{x}_1, ..., \mathbf{x}_{n-1}]$ of length $n$. Even though there are ...
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Is there a layman's explanation for why Grover's algorithm works?

This blogpost by Scott Aaronson is a very useful and simple explanation of Shor's algorithm. I'm wondering if there is such an explanation for the second most famous quantum algorithm: Grover's ...
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Grover's Algorithm and its relation to complexity classes?

I am getting confused about Grover's algorithm and it's connection to complexity classes. The Grover's algorithm finds and element $k$ in a database of $N=2^n$ (such that $f(k)=1$) of elements with $$...
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Implementation of the oracle of Grover's algorithm on IBM Q using three qubits

I am trying to get used to IBM Q by implementing three qubits Grover's algorithm but having difficulty to implement the oracle. Could you show how to do that or suggest some good resources to get ...
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How is Grover's algorithm used to estimate the mean and median of a set of numbers?

On the Wikipedia page for Grover's algorithm, it is mentioned that: "Grover's algorithm can also be used for estimating the mean and median of a set of numbers" So far I only knew how it can be ...
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How does the Grover diffusion operator work and why is it optimal?

In this answer, Grover's algorithm is explained. The explanation indicates that the algorithm relies heavily on the Grover Diffusion Operator, but does not give details on the inner workings of this ...
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Grover's algorithm: what to input to Oracle?

I am confused about what to input to Oracle in Grover's algorithm. Don't we need to input what we are looking for and where to find what we are looking for to Oracle, in addition to the ...
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Grover operator as a rotation matrix

I have seen that it is possible to represent the Grover iterator as a rotation matrix $G$. My question is, how can you do that exactly? So we say that $|\psi\rangle$ is a superposition of the states ...
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Grover's algorithm – DES circuit as oracle?

In the literature before me, the quantum oracle of the Grover algorithm is shown as a function, in which a sign change is made possible $|x\rangle\rightarrow(-1)^{f(x)}|x\rangle$. I have read that it ...
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Example of Grover's Algorithm applied to a decision problem?

I recently asked this question on Grover's algorithm, and I am still fairly confused about the whole thing. Consider the following snippet from this post (written by DIDIx13) which for convenience I ...
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Proof that Grover's operator can be written as $D_N=-H_n R_N H_n$

I am interested in showing the validity of the Grover operator. Now there are several ways to show it. One way is with complete induction. It has to be shown that the following relationship applies: $...
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Grover algorithm phase shift and steps

I am currently working on the Grover algorithm and have a few questions. In the third step of the algorithm, a phase shift is performed on all states, except $|0\rangle$. My question is, why is the ...