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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Analysis of the second Hadamard in the Detusch-Jozsa Algorithm

Consider the Deutsch-Jozsa, algorithm, which first initializes the state $|0 \rangle^{\otimes n} | 1 \rangle$, creates a superposition using the the Hadamard gate and the $U_f$ to get into the state: $...
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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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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. ...
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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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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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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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What is the intuition of using Hadamard gate in quantum fourier transform?

According to this answer by rrtucci, I still cannot catch the spirit of QFT algorithm. So I would like to ask why are we using the Hadamard gate when computing the Fourier Transform? Moreover, what ...
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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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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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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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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” ...
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155 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 ...
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50 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 ...
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1answer
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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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Can everything in QM be described with degrees instead of matrices and vectors?

I found this explanation. "The Hadamard gate can also be expressed as a 90º rotation around the Y-axis, followed by a 180º rotation around the X-axis. So $H=XY^{1/2}H = X Y^{1/2}H=XY^{1/2}$." Can ...
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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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1answer
101 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 ...
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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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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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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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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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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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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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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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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 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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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 ...
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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 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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What are the $|+\rangle$ and $|-\rangle$ states?

In the Gates Glossary of IBM Quantum Experience it states H gate The H or Hadamard gate rotates the states |0⟩ and |1⟩ to |+⟩ and |−⟩, respectively. It is useful for making superpositions. ...
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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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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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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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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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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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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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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 ...
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1answer
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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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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 ...
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Why can the QFT be replaced by Hadamard gates?

I'm studying Shor's Algorithm. In the book, author explains QFT can be replaced by Hadamard gates? Why this process is possible?? Thank you everybody. This is QPE. I attach part of book!!
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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. ...
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How do I prove that the Hadamard satisfies $H\equiv e^{i\pi H/2}$?

How can I demonstrate on the exponential part equality of the Hadamard matrix: $$H=\frac{X+Z}{\sqrt2}\equiv\exp\left(i\frac{\pi}{2}\frac{X+Z}{\sqrt2}\right).$$ In general, how can I demonstrate on: $\...
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1answer
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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 ...
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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 ...
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1answer
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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 ...