All Questions
Tagged with grovers-algorithm quantum-gate
31 questions
4
votes
2
answers
122
views
How to add the basis state $\vert 0 \rangle$ to an arbitrary uniform superposition state?
There is an unknown uniform superposition state $$\vert \psi \rangle = \frac{1}{\sqrt{N}} (\vert k_1 \rangle + \vert k_2 \rangle + \cdots + \vert k_N \rangle),$$ where $$k_1 \neq k_2 \neq \cdots k_p \...
- 41
1
vote
1
answer
143
views
3
votes
1
answer
279
views
Implementing the reflection in Grover's algorithm with $\{\mathtt{CNOT}, H, X\}$
Suppose we have a boolean function $f : \{0, \cdots, N - 1\} \to \{0, 1\}$ and want to determine $x$ such that $f(x) = 1$ given a reduced quantum oracle $V_f$ defined by
$$
V_f | x\rangle := (-1)^{f(x)...
- 53
1
vote
0
answers
48
views
How are these circuit diagrams in Grover's algorithm understood and why are they designed this way?
As shown in the figure, there are two labelled quantum states 000, 101. why are 3 $Z$-gates placed first in the phase oracle and then 2 controllable $Z$-gates in sequence?
What is the logic that makes ...
- 558
2
votes
0
answers
82
views
How to calculate number of qubits required for Grover Algorithm while constructing it's oracle and diffuser for any Specific Algorithm or Hash?
I am reading a paper titled, " (Towards Post-Quantum Secure Symmetric Cryptography:
A Mathematical Perspective)". Here, I am able to understand the gate counts and T-depth calculations. ...
1
vote
1
answer
175
views
Amplitude amplification in Grover algorithm
In "Quantum Computation and Quantum Information", they talk about Grover search. One part of the Grover search is Amplitude amplification:
But i think the red line is not true. Because i do ...
- 133
0
votes
1
answer
360
views
Quantum counting with ancillary qubits
I have been trying to implement quantum counting using my own oracle, however I've been unsuccessful getting results that make sense. The circuit I'm using looks like this (I'm only showing the ...
- 51
3
votes
1
answer
120
views
Grover's Algorithm: Why is the amplitude of $\left|a_{0}\right>$ after the second iteration $\frac{1}{\sqrt{N}}(5-\frac{20}{N}+\frac{16}{N^{2}})$?
Grover's Algorithm: Why is the amplitude of $\left|a\right>$ after the second iteration $\frac{1}{\sqrt{N}}(5-\frac{20}{N}+\frac{16}{N^{2}})$?
If I apply the Grover operator twice to the initial ...
2
votes
1
answer
343
views
Grover's Search Number of iterations for M > 1
In Grover's Search algorithm, how to determine the number of iterations for any $M$ such that $1 < M < N/2$?
The calculations given in the Nielsen and Chuang book say that $R \leq \frac{\pi}{4} ...
1
vote
1
answer
284
views
How to implement *nested* Grover search (in Quirk)?
$\newcommand{\ket}[1]{|#1 \rangle}$
$\newcommand{\bra}[1]{\langle #1 |}$
PS: I suppose this question could also ask "How to implement $2 \ket{s}\bra{s} - I$ for any (identifiable) $\ket{s} \in \...
- 374
4
votes
2
answers
654
views
Can I use Grover's algorithm for a function that has multiple arguments which satisfy it?
Let's say we have a function $f(x)$, where $f(011) = 1$, and $f(111) = 1$.
Can I still use Grover's algorithm with this function, and receive the result of either $011$, or $111$?
2
votes
2
answers
423
views
Is Grover's algorithm suitable for this search problem?
I wonder if we can utilize Grover's algorithm to solve the following search problem.
Leetcode 33. Search in Rotated Sorted Array
Example 1:
Input: nums = [4,5,6,7,0,1,2], target = 0
Output: true
...
- 237
1
vote
1
answer
458
views
Multiply-Controlled X Gate/MCT Gate Implementation
I am currently trying to implement a multi-controlled Toffoli/multi-controlled X gate in Braket, but I am confused as to the general concept of cascaded X gates and other implementations. I've read ...
- 153
0
votes
1
answer
150
views
How do two H gates act on two entangled qubits?
In this circuit, if the two qubits are initial in state 0, then after the oracle they are entangled and in state:
$0.5 * (|00\rangle+|01\rangle+|10\rangle-|11\rangle)$
My question is how do the two H ...
- 1
5
votes
2
answers
5k
views
How to understand intuitively the Grover diffusion operator?
According to the tutorial https://qiskit.org/textbook/ch-algorithms/grover.html I understand the mathematical principle of diffusion operator:
$$
\begin{equation}
\begin{split}
U_s&=2\left|s\right\...
- 175