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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 would be interested in the implications of Grover's algorithm on modern cryptography. So how is the influence of grover's algorithm on cryptography. …

How can you use Grover's Algorithm to find the shortest path? … I still want to have a brief explanation of Grover's Algorithm (i.e. Grover's algorithm in a nutshell) but didn't get a sufficient answer yet. …

I've learned about Grover's algorithm's optimal procedure, but I just read this blurb from wikipedia: Grover's algorithm is optimal up to sub-constant factors. … That is, any algorithm that accesses the database only by using the operator $U_ω$ must apply $U_ω$ at least a $1 − o(1)$ fraction as many times as Grover's algorithm. …

In other words, it seems that the qubit demands of Grover's algorithm should be $O(2^{n/2})$ to search $\{0,1\}^n$. … Doesn't this make Grover's algorithm substantially harder to implement than the classical analogue, which only uses $n$ bits? …

In the Grover's algorithm, the solution is already in the Oracle in order to mark winning state(s). I just wonder if we already know the solution, why do we need to run a circuit ? …

How can I use Grover's algorithm to do this? I've been told to encode this cost function which I'm not sure of. And to use quantum annealing to maximize the cost function. … Where does Grover's algorithm comes in this? Thanks in advance! …

Everytime I execute Grover's search algorithm on IBM real quantum computers I get a wrong answer (it doesn't find the correct winner state) unless I use only 2 qubits. … Do I need each qubit to be connected to all the other ones in the circuit for Grover's algorithm to work? Here is the Python code I am using. …

I am doing a final project on grover's algorithm, and the premise would require an extremely large number of qubits. … The probabilties of the simulators themselves are upwards of 99%, but even after a two qubit Grover's algorithm, it shows as only 40ish %? …

Grover's algorithm traditionally inputs a phase oracle, $U_\omega$ such that $U_\omega | x \rangle = (-1)^{f(x)} | x \rangle$. The task is to find some $x$ such that $f(x) = 1$. … Of course, $N$ is the number of states, $4$, not the number of bits here, as Grover's algorithm is traditionally written as. …

The input for Grover's algorithm is $n = \log_2(N=8) = 3$ qubits, where the 3 qubits encode the indices of the dataset. … There are implementations for Grover's algorithm with an oracle for $n=3$ searching for |111>, e.g. …

Scott Aaronson gives the outline of an algorithm to evaluate whether there exists a satisfying assignment for a given game tree. … The idea is to use Grover's search recursively, for each level of the tree. He notes the following problem with this approach. …

I am getting confused about Grover's algorithm and it's connection to complexity classes. … Furthermore the Grover's algorithm can be used as a subroutine. …

The Qiskit tutorial shows the application of Grover's Algorithm to solve a 2x2 sudoku. However, I don't understand how why its diffuser works as intended. …

When interpreted geometrically, the second phase of the Grover's algorithm which corresponds to inversion about the mean is interpreted as reflection over the original state. …

I am trying to solve a minimum spanning tree problem using Grover's Algorithm. … To accomplish this I would need to search a list for the minimum weight or edge for each point, for example: Given the following list: How would one use Grover's algorithm to search for the minimum …