Questions tagged [hadamard]
Single qubit Hadamard gate transforms standard basis states (zero and one states) to their superpositions (plus and minus states)
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why is $H^{⊗2}$ used to denote the parallel action of two Hadamard gates?
Why is the tensor product used here, what's its meaning? I learned tensor products as an operation between 2 matrices, and have an effect such as the follows:
How does the tensor product above relate ...
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Derivation of the effect of the Hadamard transform on a state |x⟩ in the Deutsch–Jozsa algorithm
On pg. 35 of Nielsen and Chuang, there's the following paragraph:
By checking the cases $x=0$ and $x=1$ separately we see that for a single qubit $H|x\rangle=\sum_x (-1)^{xz}|z\rangle/\sqrt{2}$.
I'm ...
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Are composite gates within superconducting hardware implemented as a single pulse or as a series of pulses?
If we have for example a gate $U^{\otimes2}$, then within superconducting hardware, is the $U$ applied onto the first qubit and then the second or is a pulse corresponding to a composite gate (tensor ...
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Applying Hadamard gate to $\sqrt{3/4}|0\rangle + \sqrt{1/4}|1\rangle$
[I am just transferring this from Stack Overflow. It might need editing.]
————
[The reader can skip to “It all sounds fine…”, before the spreadsheet representation.]
I am trying to figure out quantum ...
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Derivation for the result of performing the Hadamard transform on $|0\rangle^{\otimes n}$ being $2^{-n/2}\sum_x|x\rangle$
It's said that the result of performing the Hadamard transform on n qubits initially in the all |0> state is
$$
\frac{1}{\sqrt{2^n}}\sum_x|x\rangle
$$
where the sum is over all possible values of x....
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Represent the $n$-qubit $2^n\times2^n$ size Hadamard/quantum Fourier transform unitary square matrix as product of $k$ two-level unitary matrices
I wish to know if it is possible to express the n-qubit Hadamard unitary square matrix of size $2^n * 2^n$ as a product of 'k' two-level unitary square matrices where 'k' is of the order of polynomial ...
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How to derive the rotations caused by the H gate?
In Nielsen and Chuang, there's the following paragraph:
The Hadamard operation is just a rotation of the sphere about the ˆy axis by 90◦, followed by a rotation about the ˆx axis by 180◦.
I am ...
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214 views
Why is H gate called a ‘square-root of NOT’ gate?
In Nielsen and Chuang, there's the following paragraph:
I understand that
\begin{align*} \sqrt{NOT} =
\frac{1}{2}\left( {\begin{array}{*{20}{c}}
\sqrt 2 e^{i\pi / 4}&\sqrt 2 e^{-i\pi / 4}\\
\sqrt ...
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Initial state preparation for Hadamard test
I thought I understood Hadamard test but it seems to be shaky.
I understand that to get the expectation value $\langle\psi\ | V^\dagger|{\bf Q}|V|\psi\rangle$ we need to have gate $V$ (in blue) below ...
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Doing $|0\rangle$ then Hadamard gate then measurement
I am starting to use quantum experience and following exactly first example from lecture. After initializing the qubit to $|0\rangle$, then applying a Hadamard gate, the probability for measuring $|1\...
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How do you represent a Hadamard gate as a product of $R_x$ and $R_y$ gates?
I'm looking for a representation of Hadamard gate that uses only $R_x(x)$ and $R_y(y)$ gates. The values $x$ and $y$ may be the same, but they don't necessarily need to be.
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How to visualize Hadamard gate as $X$-$Z$-$X$ decomposition?
In the book Quantum Computation and Quantum Information by Nielsen and Chuang, chapter 4, exercise 4.4 (pg. 175), the author has asked to express Hadamard gate as product of $R_x$, $R_z$ rotations and ...
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How does a Hadamard discrete-time quantum walk result in a skewed distribution?
I was reading this tutorial about discrete random walk and got confused by the following paragraph.
After the succession of Hadamard applications ($H$), I wonder how do we get skewed distribution. I ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
45 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:
$$|...
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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 ...
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59 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 ...
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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 ...
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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 ...
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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 ...
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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 &...
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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 ...
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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 ...
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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(...
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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?
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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 ...
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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}{\...
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3answers
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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?
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1answer
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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 = \...
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1answer
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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 ...
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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.
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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 ...
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652 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:
$$\frac{|0\rangle+|1\rangle}{\sqrt 2}\langle0|+\frac{|0\...
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Calculation of the system states and the individual wire states in a quantum circuit
I am bit confused with calculating the overall state of a quantum gate and the individual wire states.
For example, lets say there are two Qubits, where Q1 is in $\frac{1}{\sqrt{2}}(\vert 0\rangle + \...
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2answers
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Generate a random bit sequence of 512 bits [duplicate]
How can I generate a random bit sequence of 512 bits on IBM Q experience using 3 or 5 qubits? Putting a hadammard gate and measuring would only give me smaller bit sequence due to limitation in number ...
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1answer
117 views
What is the matrix representation of the Hadamard gate in the computational basis?
I read about Hadamard gate H and found it's matrix representation as follows:
$$H_1=\frac{1}{\sqrt 2}\begin{pmatrix}1 & 1 \\1 & -1\end{pmatrix}$$
I wanted to know what will be the matrix ...
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Hadamard gate for three qubits; inconsistency between IBM and Matlab
I am trying to build a large and quite complex three qubit quantum circuit on IBMs quantum computer. I have a specific unitary which I am trying to implement and I am building a circuit following the ...
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What is the output of applying the Hadamard matrix to $\sum_{y\in\{0,1\}^n} (-1)^{xy}|y\rangle$?
If, for some $x$, I have the $n$-qubit state
$$\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 ...
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320 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 ...
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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 $\...
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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?
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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. ...
