Questions tagged [hadamard]
Single qubit Hadamard gate transforms standard basis states (zero and one states) to their superpositions (plus and minus states)
70
questions
3
votes
1answer
104 views
What is the relation between Hadamard transformation and QFT?
I am new to the field and I can't help having a feeling that Hadamard and Fourier Transform are somehow related, but it is not clear to me how.
Any explanation on how these two are related would be ...
1
vote
2answers
90 views
Is the tensor product of 2 Hadamard gates entangled?
Assume that you have a system of two qubits in the state $|11 \rangle$. Apply $H \otimes H$, where $H$ is the Hadamard matrix. Is the state $(H \otimes H)|11\rangle$ entangled?
I know if we take the ...
0
votes
1answer
30 views
What is the outcome when you apply 2 hadamard gates on CNOT
So when I run through risk, it displayed it had an equal 25% chance to get 00 01 10 11 respectively.
I know how the CNOT output looks like when you apply hadamard gate on control part before CNOT, but ...
0
votes
1answer
48 views
Understanding Deutsch Algorithm
From the image below, if we focus on the first qubit, we know after Hadamard (state 1) $|0\rangle$ will become $|+\rangle$ and the second qubit $|1\rangle$ will become $|-\rangle$.
What exactly would ...
0
votes
1answer
44 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 ...
6
votes
2answers
412 views
How to generalize the relationship HXH = Z for higher dimensions
Concerning the Hadamard gate and the Pauli $X$ and $Z$ gates for qubits, it is straightforward to show the following relationship via direct substitution:
$$ HXH = Z.\tag{1}$$
And I would like to ...
4
votes
1answer
68 views
Is it possible to tune the amplitude of superposition generated by Hadamard gates?
I had a question earlier about generating the superposition of all the possible states: Here. In that case, we could apply $H^{\otimes n}$ to the state $|0\rangle^{\otimes n}$, and each state has the ...
1
vote
2answers
164 views
How to describe the state of a qubit passing through two Hadamard gates? [duplicate]
Describe the state of the qubit at points A, B and C. How does this demonstrate that we need the “ket” (or the vector) representation of qubits, rather than just describing them in terms of ...
2
votes
1answer
51 views
What is a complexity of producing arbitrary equally distributed superposition?
In the article An Optimized Quantum Maximum or Minimum Searching Algorithm and its Circuits I found statement (pg. 4):
Preparing an initial state takes $\log_2(N)$ steps.
In this case the initial ...
2
votes
1answer
42 views
Is there an error on Qiskit.org textbook with the superdense coding section?
The textbook on Qiskit.org has
When the H-gate is applied to first qubit, it creates superposition and we get the state $|0+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |01\rangle)$
Shouldn't it be:
$$|...
-1
votes
1answer
135 views
What Hamiltonians generate Hadamard and CNOT? [closed]
Find a $2 \times 2$ Hamiltonian $H_H$ such that $e^{iH_H}$ equals the Hadamard matrix and a $4 \times 4$ Hamiltonian $H_{CNOT}$ such that $e^{-iH_{CNOT}}$ equals the matrix of the CNOT gate.
I have ...
2
votes
1answer
57 views
How does $U_f$ act on a qudit state in the Deutsch-Jozsa Algorithm
The problem starts with the given the input state $|\psi_{in} \rangle = |0 \rangle |1 \rangle$, I'm asked to calculate $|\psi'\rangle = H_d \otimes H_d |\psi_{in} \rangle$ where $H_d$ is the Hadamard ...
3
votes
2answers
70 views
Show that the two circuits are equivalent mathematically
This exercise wants me to prove the equivalence of the two circuits using their mathematical representations.
Circuit 1:
Circuit 2:
Circuit 1 (q1 CNOT ...
5
votes
2answers
116 views
Show that the Hadamard gate is equivalent to a 180 degree rotation of a certain axis
Show that the Hadamard gate is equivalent to a 180 degree rotation about the axis defined by $(\vec{e_x} - \vec{e_z}) / \sqrt{2}$ where $\vec{e_x}$ and $\vec{e_z}$ are unit vectors pointing along the ...
2
votes
1answer
105 views
How does the outcome of measurement of a qubit change when we use different basis despite the system hasn't changed? [closed]
Let's assume that the quantum state of the system is written in a standard basis {$|0\rangle, |1\rangle$} and when we performed a measurement we got $|0\rangle$ as an outcome of measurement so we ...
3
votes
1answer
56 views
Mistake in using dirac notation when applying $X$ gate to vector
The X gate is given by $\big(\begin{smallmatrix}
0 & 1 \\
1 & 0
\end{smallmatrix}\big)$ in the computational basis. In the Hadamard basis, the gate is $X_H = \big(\begin{smallmatrix}
1 &...
3
votes
1answer
63 views
Measuring in the computational basis in the single qubit gate QFT implementation
I've come across this paper about a single-qubit-gate-only QFT implementation. In the paper it is claimed that measuring a qubit after applying the Hadamard gate (it isn't called Hadamard gate in the ...
1
vote
1answer
75 views
A CNOT between two Hadamard gates: why does the CNOT changed the output of the second Hadamard gate?
Applying the Hadamard gate twice in a row, it restores the original input:
https://algassert.com/quirk#circuit={%22cols%22:[[%22H%22],[%22H%22]]}
However, if a CNOT control is added between the two ...
4
votes
1answer
39 views
Definitions of $D_y$ gate in Hamiltonian simulation: are they the same?
I'm reading a Hamiltonian simulation example proposed in this paper. From their notation, the operator $D_y$ (sometimes it's called $H_y$) serves the function to diagonalize the Pauli matrix $\sigma_y(...
3
votes
2answers
103 views
Transforming $|100\rangle$ state into $|000\rangle + |111\rangle$ state using only Hadamard and CNOT gates
Hi, How to convert $|100\rangle$ 3-qubit quantum state into $\frac{1}{\sqrt{2}}(|000\rangle + |111\rangle)$ state using only Hadamard and CNOT gates? Also, is output state an entangled one?
3
votes
3answers
138 views
How are the IBM's and Google's Hadamard gates fabricated and operated?
There are thousands of articles, books and web sites describing the Hadamard Gate from a theoretical point of view.
But I haven't been able to find any photo about any real implementeation of a ...
2
votes
2answers
117 views
Transforming $|01 \rangle + |10 \rangle - |11 \rangle \to |01 \rangle - |10 \rangle + |11 \rangle$
How to convert from current state: $$|\psi \rangle =\dfrac{ |01 \rangle + |10 \rangle - |11 \rangle}{\sqrt{3}}$$
into a target state
$$|\phi \rangle = \dfrac{|01 \rangle - |10 \rangle + |11 \rangle}{\...
1
vote
3answers
86 views
Why 2 $H$ gates in series create a probability of 100% for one value of the qubit and 0% of the second value of the qubit?
Why 2 $H$ gates in series create a probability of 100% for one value of the qubit and 0% of the second value of the qubit since an $H$ gate acts like a superposition generator?
3
votes
1answer
92 views
Confused about the application of Hadamard gate to uncorrelated qubits [duplicate]
Why does applying the following circuit on a $00$ state produce
$|0\rangle \otimes |+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |01\rangle)$. Shouldn't it produce $ |+\rangle \otimes |0\rangle = \...
3
votes
1answer
69 views
Is there a clear boundary between quantum coupling and quantum entanglement?
I have a few questions in understanding the difference between coupling and entanglement in quantum systems: Is there a clear boundary between quantum coupling and quantum entanglement? If two quantum ...
1
vote
2answers
184 views
How do I apply the Hadamard gate to one qubit in a two-qubit pure state?
So in lectures I see lots of these:
And somehow I intuitively understand it (at least for the 1 qubit case), but I don't understand the math – especially for 2 qubits.
1
vote
3answers
102 views
How do I apply a Hadamard gate on a given qubit, in matrix formalism?
Hadamard gate matrix is:
$$\frac{1}{\sqrt2}\begin{bmatrix}1 & 1 \\ 1 & -1\end{bmatrix}$$
The matrix for $|0\rangle$ is:
$$\begin{bmatrix}1 \\ 0\end{bmatrix}$$
I am unable to understand, how ...
3
votes
1answer
556 views
How to translate the Hadamard gate matrix into Dirac notation?
Hadamard gate matrix is:
$$\frac{1}{\sqrt 2}\begin{bmatrix}1 && 1 \\ 1 && -1\end{bmatrix}$$
The Dirac notation for it is:
$$\frac{|0\rangle+|1\rangle}{\sqrt 2}\langle0|+\frac{|0\...
1
vote
2answers
54 views
Calculation of the system states and the individual wire states in a quantum circuit
I am bit confused with calculating the overall state of a quantum gate and the individual wire states.
For example, lets say there are two Qubits, where Q1 is in $\frac{1}{\sqrt{2}}(\vert 0\rangle + \...
0
votes
2answers
100 views
Generate a random bit sequence of 512 bits [duplicate]
How can I generate a random bit sequence of 512 bits on IBM Q experience using 3 or 5 qubits? Putting a hadammard gate and measuring would only give me smaller bit sequence due to limitation in number ...
0
votes
1answer
106 views
What is the matrix representation of the Hadamard gate in the computational basis?
I read about Hadamard gate H and found it's matrix representation as follows:
$$H_1=\frac{1}{\sqrt 2}\begin{pmatrix}1 & 1 \\1 & -1\end{pmatrix}$$
I wanted to know what will be the matrix ...
1
vote
1answer
64 views
Hadamard gate for three qubits; inconsistency between IBM and Matlab
I am trying to build a large and quite complex three qubit quantum circuit on IBMs quantum computer. I have a specific unitary which I am trying to implement and I am building a circuit following the ...
0
votes
1answer
106 views
What is the output of applying the Hadamard matrix to $\sum_{y\in\{0,1\}^n} (-1)^{xy}|y\rangle$?
If, for some $x$, I have the $n$-qubit state
$$\sum_{y\in\{0,1\}^n} (-1)^{xy}|y\rangle,$$
and I would like to apply to that the $n$-qubit Hadamard transform, with the aim of calculating the final ...
4
votes
2answers
275 views
Hadamard Test to calculate imaginary part
I am trying to understand the Hadamard Test by finding the average value of $U_1$, which is a diagonal matrix with $1$ everywhere except on the first element.
I performed the regular Hadamard Test as ...
1
vote
1answer
63 views
Hadamard direct mapping of input to output in $\theta$ and $\varphi$ form
I was wondering what would be an equation for Hadamard operation for a single qubit, given the input as the current $\theta$ (0 to $+\pi/2$) and $\varphi$ ($-\pi$ to $+\pi$) and output expected in $\...
1
vote
1answer
70 views
What are the I, X, Z gates in quantum gates? [closed]
Can someone please explan how the $\rm I$, $\rm X$ and $\rm Z$ gates work?
If $\rm{I = X^2 = Z^2}$, can you explain why this is the case or why it wouldn't work?
0
votes
1answer
80 views
How to undo an operation in qiskit on jupyter notebook?
I am not able to undo an operation. For example, I want a single Hadamard gate on a single qubit but by mistake two Hadamard gate added. Now I want to remove one of them without interrupting kernel. ...
2
votes
1answer
50 views
Prove that QFT and Walsh-Hadamard gates give the same output when acting on $\lvert x\rangle\lvert 0\rangle$ [duplicate]
I know that $QFT_n|0\rangle$ is equivalent to $H_n|0\rangle$
(mathematical proof).
And it is also easy to prove that $QFT_1$ is equivalent to $H_1$ (applied to one QuBit).
From looking at the circuit ...
2
votes
1answer
114 views
N-Qubit Hadamard vs Quantum Fourier Transform
Both Simon's algorithm and the algorithm for period finding begin by placing qubits in the equal superposition state, but Simon's algorithm uses the n-qubit Hadamard $H^{\otimes n}$ while the period ...
2
votes
2answers
130 views
Why do we divide by $\sqrt2$ in the qubit states $\lvert\pm\rangle=\frac{1}{\sqrt2}(\lvert0\rangle\pm\lvert1\rangle)$?
I have a very basic question. I have found qubits are represented as complex vectors. I get it totally. I understand bracket notation and vector\matrix algebra. However, I cannot move further from ...
2
votes
1answer
50 views
Randomness using simple parallel Hadamard circuit
I've recently tried to build a Random generator using 5 hadamard gates (shown as U2 below) measured to 5 classical bits in parallel as shown in the circuit image.
I've executed this circuit for 8192 ...
6
votes
0answers
235 views
Hadamard Overlap Test
I am trying to understand a test called Hadamard Overlap Test, which consists of a destructive swap test (section IV of swap test and Hong-Ou-Mandel effect are equivalent) right after a Hadamard test. ...
1
vote
2answers
475 views
Is there a gate that puts a qubit into superposition with a not so purely probabalistic (50 50) outcome?
I know that a Hadamard states is a purely probabalistic one; e.g.
$$H\vert 0\rangle=a\vert 0\rangle+b\vert 1\rangle$$
where $a^2=0.5$ and $b^2=0.5$.
Are there any states in which the ...
2
votes
1answer
80 views
Hadamard gate with two inputs in the circuit for the BB84 protocol?
I am reading the book "Quantum Computing verstehen" by Matthias Homeister.
At the moment i'm having a look at the BB84 protocol (which is described in kind of an abstract way).
In this chapter a ...
2
votes
1answer
21 views
How can I make qiskit output raw data?
I am new to quantum computing, and I want to make a program to output 0 or 1 randomly by Hadamard gate, and use that information to make a GUI interface. For example, a coin flip program that output "...
2
votes
1answer
80 views
Probabilities does not sum up to 1 in simple circuit
I have an issue, perhaps with normalization with the following state. For $\alpha^2 + \beta^2 =1 $, the probabilities in this state does not sum up to 1.
$$|\psi\rangle := \frac{1}{2}\left[\alpha\...
1
vote
2answers
95 views
What happens if $|\psi\rangle$ = $|0\rangle$ or $|\psi\rangle$ = $|1\rangle$ is passed as an input to two Hadamard gates in sequence?
I'm a computer science student and soon I will have a math exam. I'm really struggling with this preparation question. Also, includes the following:
How does this demonstrate that we need the “ket” ...
3
votes
1answer
55 views
$H = e^{i\pi/4} \sqrt{iNOT}$?
In the paper Valley qubit in Gated MoS$_2$ monolayer quantum dot, a description of how a $NOT$ gate would be performed on a qubit in the described device is given.
The authors say that in the ...
1
vote
1answer
302 views
Simple algebraic explanation for normalizing states
I'm wondering how a set of three 0-state qubits, each prepared identically, like so:
When considered together, may produce the fraction:
along with their combined states.
This is the entire circuit....
4
votes
2answers
1k views
How should I understand the change of qubit's basis as a rotation?
I have a little difficulty with understanding. How do I properly visualize the change of qubit's basis as a rotation?
Let's say that we have classical basis vectors, $|0\rangle$ and $|1\rangle$. Now, ...
