# 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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### Different result between Q# and Qiskit

I'm running a search program with custom initial state. I wrote a program in Q# and one in Qiskit but I get different results even if the code seems to be peforming the same operations. The Q# result ...
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### Why does Grover's Diffusion Operator have the word “diffusion” in its name? [duplicate]

Where do I see the diffusion in the Grovers operator? I would think there should be an analogy to classical diffusion but I am not able to see the correspondence.
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### Grover algorithm in Q#

I have this program derived from Microsoft Quantum Kata for quantum search (Grover algorithm) (see here) ...
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### Can one use a quantum circuit as a pathfinding algorithm?

I've been learning about quantum computing, and I noticed that another way to describe the state vector is as a path in a binary tree where each level of tree represents another qubit, each node ...
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### Alternative Grover's Diffuse Operator [duplicate]

I was wondering if there is any good references where I could read to understand the construction of Unitary Operators such as the Diffuse Operator in Grover's Algorithm. I am looking to build my own ...
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### Lemma 1 in the paper by Brassard, Hoyer, Tapp (1998) on Quantum counting

In the paper by Brassard, Hoyer, Tapp (1998) on Quantum Counting we have the following expression for the state: $$|Y\rangle =\sum_{i\in\mathbb{Z}}x_i|i\rangle |Y_i\rangle.$$ Now we have a quantum ...
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### Grover's 3-qubits tutorial: Why we need the last X gates

I'm following the tutorial in Grover's Algorithm - Example 3 qubits I'm trying to understand the amplitude amplification using the reflection. But I cannot understand if we really need the step 3d (...
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### How exactly does a chaotic amplitude amplifier work?

In this link (the bottom presentation) is described an application of Grover's algorithm for 3SAT (and a possible quantum version of Shoning's algorithm for 3SAT). I can find my way through the ...
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### What to do when the amount of solutions is not known before applying Grovers Algorithm?

When running Grovers Algorithm one has to know how many solutions there are right? When the number of solutions are not known is then what do you do then?
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### How can you decompose Grover's diffusion operator into gates?

I know how Grover's diffusion operator works ($U_s = 2|s\rangle\langle s|-I$) with the inversion around the mean. However, I want to implement it in simpler gates, to use the algorithm. How can I do ...
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### Can anyone provide me with an example of the for Grover's algorithm on one qubit?

I'm having trouble understanding Grover's Algorithm, so I'd like to start with the case with 1 qubit. But I don't see anyone build it for 1 qubit, only 2 is the minimum. Is it because that's ...
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### Can we use different oracles for each (extended) Grover iteration?

Within the context of Grover's algorithm,  if there are  $N/4$  elements marked instead of just one ($N = 2^n$) , if we run one iteration of Grover's algorithm (one phase inversion and one inversion ...