# 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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### Grover search with single query to $f(x)$ and multiple queries to $f(x) = a$

Assume $f(x)$ is an $n$ bits to $m$ bits function and we want to use Grover's search algorithm to find $x$ such that $f(x) = a$, where $a$ is some $m$-bit predetermined value. When using the ...
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### Grover's algorithm returns skewed probability distribution

I wrote an implementation of Grover's algorithm that looks like this: ...
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### Grover's algorithm and RSA from Nielsen

Nilsen states that one can define a function for the oracle in the Grover algorithm, which is constructed as follows. So there is a number $m$ that consists of $p$ and $q$ (both primes) $m = pq$. Now ...
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### Grover's algorithm and Battleship solution

I have read that quantum computers are not known to be able to solve NP-complete problems in polynomial time. However, if you consider a game of Battleship with grid size $X, Y$ and represent this by ...
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### Counting in Q#: number of solutions

I have this program derived from Microsoft Quantum Katas for counting (see here): ...
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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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### How is the Grover-Algorithm applied to a database?

Question I want to use the Grover-Algorithm to search an unsorted database for an element $x$. Now the question arises, how do I initialize index and value of the database with the qubits? Example ...
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### Grover's algorithm: number of searches

I would like to start my question with a quote: If an encrypted document and its source can be obtained, it is possible to attempt to find the 56-bit key. An exhaustive search by conventional means ...
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### Consequences of Grover's algorithm

I want to look more closely at the consequences of the Grovers algorithm. As is well known, the algorithm provides a quadratic improvement compared to classical search algorithms. Specifically, I ...
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### Is the $|-\rangle$ state the only one that can do the trick for Grover's algorithm?

$\newcommand{\qr}[1]{|#1\rangle}$Grover algorithm's input is a superposition, representing the haystack, and the Bell state $\qr{-}$. The $\qr{-}$ seems utterly important: when I replaced $\qr{-}$ by,...
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### What can be a mini research project based on Grover's algorithm or the Deutsch Jozsa algorithm?

I need to work out a research project on quantum computing as a part of my curriculum. I was wondering how to implement something theoretically with the basic knowledge I have. I have learned about ...
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### What is the complexity of the quantum phase estimation in Grover's algorithm?

Suppose we are using GA (Grover's algorithm) such that we are given it has 2 or more solutions. The search space is of size $N$. We all know Grover's algorithm has, at worst, a time complexity ...
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### Current limits on Grover search space

I was wondering why till date Grover search has been implemented only till 3 qubits (corresponding to size of database = 8). Refer this paper The reason why I ask is that we have much larger sized ...
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### How significant are the variants of Grover's Algorithm?

I found a paper by Grover titled "How significant are the known collision and element distinctness quantum algorithms?", in which he expressed criticism to several famous algorithms, including ...
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### Why is Grover's algorithm not converging monotonically? (Python implementation)

I have tried to implement Grover's algorithm for three qubits in python/numpy and the first two iterations work like a charm but the third one starts to diverge. Is this expected, or is there a bug in ...
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### Grover algorithm for more than one element

I am currently working on the Grover algorithm again. In many lectures and documents, as well as books, I noticed that there is always talk of looking for a single element of $N$ elements. Now I read ...
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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 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 ...
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### Correspondence between the Topological model and Quantum Circuit model

For example, given the $R$ & $F$ gates and Toric codes for a given problem, how to convert this code into the conventional circuit model and vice versa. From the literature developed, it seems ...
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### Is there any (really) quantum procedure that's an algorithm and not a Las Vegas algorithm?

Let me take Grover's algorithm as an example. In most cases, Grover's algorithm is able to yield with a high probability the desired term of the superposition. When the superposition has more than 4 ...
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### Grover's algorithm with W-state

In the general form of Grover's algorithm, we start with the uniform superposition of n qubits. Now, suppose instead that we start with a generic state, for example ...
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### In amplitude amplification, how are the amplitudes of qubits changed?

I am relatively new to quantum computing and I feel like I don't fully understand the power of quantum computing due to a lack of understanding of how amplitude amplification works. What is ...
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### Can adiabatic quantum computing be faster than Grover's algorithm?

It has been proven that adiabatic quantum computing is equivalent to "standard", or gate-model quantum computing. Adiabatic computing, however, shows promises for optimisation problems, where the ...
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### Speedup Prange ISD using Grover

In his 2009 paper, Grover vs McElicee, Bernstein proposed to use the Grover's algorithm to obtain a quadratic speedup on the Prange ISD. However, it is not quite clear to me in which part of the ...
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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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### Quantum attack on hash functions

The line of questioning is inspired by the pick one trick in Section 4 of the PDF version of the paper Quantum Attacks on Classical Proof Systems - The Hardness of Quantum Rewinding (Ambainis et al., ...
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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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### Can we speed up the Grover's Algorithm by running parallel processes?

In classical computing, we can run the key search (for example AES) by running parallel computing nodes as many as possible. It is clear that we can run many Grover's algorithms, too. My question is;...
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### Why does Grover's search invert about the mean?

Let $\vert s\rangle = \frac{1}{\sqrt{N}}\sum_{i=1}^N\vert x_i\rangle$ be an equal superposition over states from which we need to find one solution state $\vert w\rangle$. The phase flip operator in ...
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### How many qubits does it take to break a 10 characters password?

Let's assume we developed a hashcat-like programs for quantum computer. How many qubits we need to find the correct hash (WPA, MD5,...) from a 10 characters password make from upper, lower & ...
I'm fairly confused about how Grover's algorithm could be used in practice and I'd like to ask help on clarification through an example. Let's assume an $N=8$ element database that contains colors ...