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.
432 questions
1 vote
1 answer
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Why is the fastest quantum time complexity of unstructured search O(sqrt(n))?
Recently, I have watched video on 3Blue1Brown about Grover's algorithm. He give an example that: To find a secret number in the range from 0 to n−1, you can query a hidden function that returns “true”...
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3 votes
0 answers
62 views
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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3 votes
2 answers
278 views
Can't figure out Telescoping Sum Trick in Proof
I was reading the fantastic paper "Grover’s algorithm is an approximation of imaginary-time evolution" (https://arxiv.org/abs/2507.15065) and there's a step in their proof that I can't ...
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2 votes
1 answer
145 views
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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0 votes
1 answer
100 views
How to construct an oracle and flips the phase of the solution bit strings?
I am trying to solve the boolean problem (x1 or x2) and (~x1 or ~x2 or x3) using Grover's algorithm. The only measured bits are q0, q1, and q2. This is my oracle: ...
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2 votes
1 answer
105 views
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 ...
0 votes
0 answers
62 views
How to make a phase oracle that marks the largest number?
I have a list of strategies each with a corresponding score, I want my oracle to apply the phase shift on the strategy with the largest score value. Without knowing the values beforehand how would I ...
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0 votes
1 answer
181 views
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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3 votes
1 answer
134 views
How to describe the phase detection operator of the adaptive GROVER algorithm mathematically?
After reading document https://link.springer.com/chapter/10.1007/978-3-319-11857-4_41, I have been curious about the mathematical expression of the phase detection operator. I searched for articles ...
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1 vote
1 answer
134 views
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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1 vote
2 answers
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Is it possible to entangle two qubits (by means of Grover techniques)?
Given two separate states, I'd like to entangle them to a specific configuration. Example 1: $$|+\rangle \otimes |+\rangle \rightarrow \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$$ Example 2: $$(a_1|0\...
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3 votes
1 answer
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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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3 votes
2 answers
954 views
Grover's algorithm number of iterations
I am trying to understand Grover's algorithm without much of a background in quantum. I believe I understood the main parts to be: The quantum state is initialized to represent all $n$ possible ...
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-2 votes
1 answer
251 views
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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0 votes
1 answer
181 views
Grover's algorithm in Qiskit, problems with growing number of qubits
I am building a n-qubit circuit for Grover's algorithm using the material on Qiskit Github as a guide. https://github.com/Qiskit/textbook/blob/main/notebooks/ch-algorithms/grover.ipynb In particular I ...
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