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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Does Knowing a bound for the number of solutions allow for any improvement for the Quantum counting algorithm
Recently, I've been looking at the Quantum Counting Algorithm, derived from Grover's algorithm in (https://arxiv.org/pdf/quant-ph/9605034).
Background:
I got especially interested in, if the prime ...
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Grover's algorithm oracle is the classical Householder reflection?
I am learning Grover by reading the lecture notes https://www.cs.cmu.edu/~odonnell/quantum15/lecture04.pdf
It assumes the availability of an oracle gate $O_f$ that provides the following output:
$$
- \...
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Grover's Algorithm oracle for finding an 8-bit key
I've been trying around different things with Grover's algorithm, and would want to experiment a practical scenario with it by building an oracle to find an 8-bit key.
Very shortly explained, my ...
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Logical error on Grover's Algorithm protected by Shor's error correction
Hey guys I need some help figuring out why this code will not return the correct keyed result
Basically it is Gorver's Algorithm that is protected by Shor's error correction but when run '000' always ...
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How is Grover's algorithm faster than an apples-to-apples classical version?
Nearly every time I've read about Grover's algorithm, there is an introduction to the equivalent classical algorithm. It goes something like this:
You're searching for a hidden integer that only a ...
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Simplifying the Grover's algorithm
I am learning quantum computing as a beginner and have a question about the Grover’s algorithm (perhaps a naive question). I understand that the key of the Grover’s algorithm is to iteratively use a ...
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Is Grover's Algorithm useless?
If I know what oracle to implement, I know what is the state that I am searching for, so why should I use this algorithm?
I mean, if my quantum control system knows how to implement the oracle, it ...
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Quantum Monte Carlo and Quadratic Speedup
In classical Monte Carlo, when we want to predict a value for something which has inherent uncertainty, such as predicting a stock value, we use a mathematical model like Geometric Brownian Motion and ...
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Coding Oracle for Grover's Algorithm - Qiskit
I am looking to create an oracle that marks the solution states by checking the arrays entries(1 column and many rows) with a threshold. If the value in the array is greater then the threshold the ...
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How to solve "Maximum allowed dimension exceeded" while trying to run Grover's algorithm in IBM backend?
I am trying to run Grover's algorithm on IBM backend. The previous code was running fine but due to some recent changes in qiskit, I had to modify it. But I can't seem to fix this "Maximum ...
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Step by step explanation of Grover diffusion operator quantum circuit for 2 qubits
I am a newbie to quantum computing and recently came across Grover's algorithm. I'm now trying to understand its quantum circuit for 2 qubits.
I have understood the oracle which marks the correct ...
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Constructing Conditional Phase Shift in Grover's Algorithm and Optimality of Grover's Algorithm for Multiple Solutions
I’m currently working through some questions related to Grover's algorithm and need help with the following:
Conditional Phase Shift Construction using single qubits and two-qubits gate? Also, how ...
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Grover's algorithm: Build the uniform quantum state over all $n$-bit strings
I am visualising the set $A_1$ as given in the IBM presentation found here: Grover's algorithm. In the presentation, this set is defined by the following expression:
$$A_1 = \{ x \in \Sigma^n: f(x) = ...
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Implementation of the Grover's oracle in a real life use case
Imagine a database of DNA fingerprints, each one characteristic of only one person. You
are given a DNA trace and asked to find the person to which it belongs. There is no way
(to my knowledge !) to ...
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Why is an exponential scaling chosen in the Grover Algorithm for an unknown amount of solutions?
In "tight bounds on quantum searching" by Boyer et al., an exponential scaling for the upper limit of the interval is presented, that is some number $\lambda^s$. This number is the upper ...
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Qiskit Grover search with QasmSimulator
I'm working through a Qiskit tutorial on Grover search. Unfortunately it was published in 2023 and the tutorial's version of Qiskit (earlier than v1.00) is now out of date. I tried to rewrite the ...
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Understanding sources of error in 4-bit Grover's search on IBM QC
This question is similar to some others I've come across, related to why a 4-qubit implementation of Grover's search yields such poor results when run on the IBM QC compared to the 3-qubit case (...
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Quantum algorithm for finding minimum $x$ such that $f(x)=1$
I am currently working on a project which includes the comparison of strings in $O(\sqrt{n})$ complexity where $n$ is the length of the string. The reference for this algorithm can be found in ...
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Confusion on the Quantum Minimum Finding Algorithm
I am a new beginner in quantum algorithms. Recently, I was trying to learn the quantum minimum finding algorithm appeared in here. I am struggling to fully understand the operations in the algorithm.
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Applying cz gate in oracle for Grovers Algorithm
Theoretically say I have a 2 qubit circuit where the solution state is |11>. I was watching a video from qiskit (https://www.youtube.com/watch?v=0RPFWZj7Jm0) on this and in the oracle they only ...
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Why does "Read the Fine Print" say that a quantum computer can "maybe" achieve a modest speedup for optimization problems?
Quantum Machine Learning Algorithms: Read the Fine Print says:
By using a quantum computer,
one could dramatically accelerate the simulation of quantum physics and chemistry (the original application
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Cannot get a correct quantum count for a sudoku example
I've implemented a quantum counting algorithm for a sudoku example by following
the amplitude estimation algorithm introduced in Mosca's textbook (An Introduction to Quantum Computing, page#172):
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Grover with randomized oracle
I'm sorry if this is a stupid question. I want to know about the behavior of Grover's algorithm with oracle having a low one-sided probability of error. So if $f(x)=0$ my oracle returns $0$ and if $f(...
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How to perform amplitude amplification when the initial amplitude of aiming state is unknown
Let's say, I want to perform amplitude amplification on the quantum state
$$|s\rangle=\sum_{i=0}^{2^n-1}m_i |i\rangle\,,$$
And the aiming state is $|x\rangle\,.$
Usually, when I perform amplitude ...
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State amplification in Grover when starting with W state
I have two 3-qubit registers, each one is prepared in $W$ state, so my two registers are in state: $$\left|W_3\right\rangle\otimes \left|W_3\right\rangle \ ,$$I use this (6-qubits) diffusion operator ...
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