# 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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### How to extract key from a Grover's attack?

I have implemented a lightweight cipher on a quantum circuit, Now, by implementing oracle and amplifying I can increase the probability of the marked ciphered state. While there is no mechanism to ...
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### Get confused about the implementation of Amplitude Amplifier

I have a circuit $A$, which produces $$A|0^n\rangle _a |00\rangle _b = \phi_0 |00\rangle _b + \phi_1 |01\rangle _b+ \phi_2 |10\rangle _b + \phi_3 |11\rangle _b$$ And only $\phi_0 |00\rangle _b$ is ...
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### Can Amplitude Amplification amplify an unknown state? [duplicate]

If you have for example the basis states $|000\rangle$ and $|xxx\rangle$. The value of the second basis state is unknown, but the amplitude of both states is given. Also the amplitude of the second ...
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### Derivation of energy gap formula for adiabatic Grover algorithm

I am having a difficulty in finding the full derivation for local search energy gap, as described in In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?. I looked ...
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### Why doesn´t Grover's Algorithm work for my Qiskit circuit?

I built a circuit in Qiskit with two GHZ states. In the beginning, I created the superposition $\sim\bigg(|0000\rangle+|0101\rangle+|1010\rangle+|1111\rangle\bigg)$ with two $H$s, and two $CNOT$s. Now,...
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### Minimum probability of measuring marked state in Grover's algorithm is 1/8

I recently came across the proposition that for a database containing $N$ elements with $m<\sqrt{N}$ marked elements, applying Grover's algorithm with any $T$ $(0<T<\sqrt{N}-1)$ iterations (...
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### How to implement Gover's algorithm with unknown number of solutions using qiskit or pennylane?

In general Grover's algorithm has a fixed number of solutions. But in special cases, we can't know the exact number of solutions, even the solutions change over time. So how to construct oracle in ...
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### Quantum algorithm for AES?

We all know about Shor's algorithm to attack RSA but what is the state of the art for attacking symetric algorithm such as AES today with quantum computers ? What are the most promising papers on this ...
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### Quantum circuit implementation of shift operator in quantum walk

I'm considering discrete-time quantum walk on $2\times2$ grid with periodic quantum walk. In particular focus on shift operator which has the form : S|i,j\rangle \otimes |x,y\...
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### Generalization of optimality of Grover's algorithm for an arbitrary number of marked elements

In the final remark Zalka's paper about the proof of exact optimality of Grover's algorithm for the search problem with a single marked state, we have the following suggestion for future work: "...
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### How are these circuit diagrams in Grover's algorithm understood and why are they designed this way?

As shown in the figure, there are two labelled quantum states 000, 101. why are 3 $Z$-gates placed first in the phase oracle and then 2 controllable $Z$-gates in sequence? What is the logic that makes ...
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### An unexpected result of the Implementation of a finding minimum values algorithm using a qRAM

Motivated by the article Quantum algorithm for finding minimum values in a Quantum Random Access Memory, I'm training to implement a simplified version of the proposed algorithm. But the output isn't ...
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### Please teach the construction law of oracle $U_f$ in Grover’s algorithm

The framework of Grover's algorithm is shown in Figure from Qiskit. https://learn.qiskit.org/course/ch-algorithms/grovers-algorithm But I didn't understand the tutorial's construction rules for $U_f$. ...
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### Using Classiq for Grover Search

I am participating Classiq Bootcamp, First lesson here, and I need to implement Grover Search in a specific result that satisfies few constrains: The circuit should encompass a minimum of two Grover ...
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