# 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 Iteration

I have two questions regarding a search algorithm based on the Grover Iteration. Lets assume I would have a classical database: ...
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### Mark a state if it is part of another register

I am wondering something, especially about Grover algorithm: imagine I have a quantum register $a$ and a quantum register $b$ of equal length. Then, suppose I apply some algorithms on $a$ s.t. it is ...
1 vote
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### Hadamard gate in Grover algorithm

What is the need to apply the Hadamard gate as the first step while designing the diffuser circuit in the implementation of Grover's algorithm? I know what the gate does but I cannot understand what ...
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### Grovers algorithm: Diffuser on a state that isn't a linear superposition of all possible states

I've been trying to get Grover's algorithm to work, where part of the qubits have been measured, before Grovers is iterated. I have found a circuit that works, but I don't get why it does. I have ...
1 vote
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### Reflection operator in amplitude amplification for block encoding

I am trying to figure out equation (2.33) here. Given that \begin{gather} U_{\psi_0}|{0^m}\rangle|{0^n}\rangle=\sqrt{p_0}|{0^m}\rangle|{\psi_0}\rangle+\sqrt{1-p_0}|{\perp}\rangle,\\ (\Pi\otimes I_n)|{\...
1 vote
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### Quantum algorithm to determine the existence of a solution

Consider two vectors $u$, $t$ living in some space (let's say $ℝ^{n}$), and the following (simple) problem: Find a vector $v$ such that $∃a,b\inℝ$, $au+bv=t$ Imagine I want to use Grover to find a ...
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### Grover search with index register entangled with ancilla

I have a question: when Grover's search is set up with ancilla qubits in an entangled state, does it still work or not? Consider an example with a 4-size search space. Firstly, we use 2 qubits ...
1 vote
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### How do I use the quantum searching algorithm to loop search through a datafile in qiskit?

I have a localhost index.html has a table contains names and address and balances etc... also there is a search bar on the home page to go through the pages, the interesting thing is, there is loooot ...
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### Amplitude amplification with or without ancilla state

I am trying to understand amplitude amplification and I am able to find two formulations (almost identical). (A) No ancilla Usually, and what I do understand quite well, is that you start with the ...
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### SOlving SAT problem having Boolean And f(x) = x1 and x2 and (not x3) using Grover's algorithm

Solving SAT using Grover's algorithm , if the f(x) = x1 and x2 and (not x3). I have a few questions: is this considered a 3 SAT problem as there are three literals here and one clause? I have seen ...
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### Amplifying states using partial information

Assume we have an initial state $(H^{\otimes n}|0\rangle)|0\rangle = \frac{1}{\sqrt{N}}\sum_{i=0}^{N-1}|i\rangle|0\rangle$ in two $n$-qubit registers (let $N=2^n$). Then we feed this state through a ...
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### Grover search in Quantum Computation and Quantum Information (Nielsen and Chuang)

in Nielsen and Chuang's book in Box 6.1 (page 256 for 10th edition) there is a example of Grover's search algorithm for 3 qubits (2 as search space + 1 for oracle). I am currently trying to implement ...
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### Using Grover on entangled states

I am trying to implement Grover's algorithm on an entangled state. The idea is that I will have a state $\sum_x\alpha_x|f(x),x\rangle$ and I want to measure the $x$, for which $f(x)=0$. Note that $f$ ...
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### Accuracy of Grover algorithm is 100% for 2 qubit, 94.5% on 3 qubit and 96.2% for 4 qubit on simulator. Why it decreasing and then again increasing?

The accuracy of Grover's algorithm decreases for 3 qubit then increases for 4 qubit and then again increases for 5-qubit on simulator (qasm simulator) with pi/4(sqrt N) iterations. What is the reason ...
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### Is it possible to run the Grover algorithm under specific condition

The Grover algorithm deals with sorting in an unstructured database and we can build an oracle (target function f) to achieve this. The oracle returns 1 if the element we search is founded otherwise 0....
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### Is the execution of a circuit neglectable for large optimization problems?

Assume a large combinatorial optimization problem should be solved (e.g. via Grover) and further assume there is a (near error free) universal quantum computer with a sufficient number of qubits (and ...
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### How to verify a matrix-vector product with Grover search?

I am looking at the Ambainis et al. method of verifying whether $AB = C$ in $O(n^{7/4})$ queries, as described in Buhrman and Špalek. They have the following sentence: verify the matrix-vector ...
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### Does the diffusion operator change when there are multiple iterations of the Grover cycle?

My question relates to the theoretical application of the diffusion operator in Grover's algorithm. I understand that a single Grover iteration on an equal superposition will change the amplitude of ...
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### Phase Oracle in Qiskit Solving Satisfiability Problems using Grover's Algorithm Section

In Qiskit Textbook, there is a section on solving satisfiability problems using Grover's Algorithm. For the 3SAT instance they construct the following phase oracle: Is there any reasoning behind ...
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### In generals Amplitude Amplification algorithm, the initial state does not need to attain equally superposition?

In the beginning of this paper about amplitude amplification algorithm, the author stated the conventions of amplitude amplification which I quoted the important part for your convenience as follows: ...
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