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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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 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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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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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. ...
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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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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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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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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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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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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 ...
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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 "...
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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\...
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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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$H = e^{i\pi/4} \sqrt{iNOT}$?

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 ...
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159 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....
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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, ...
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Hadamard/Phase/Hadamard and Inversion about the Mean

I understand the matrix multiplication behind Grover's algorithm, but I'd like to get an intuitive grasp on why sequence of gates Hadamard-Phase-Hadamard does inversion about the mean. Can anyone help?...
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How to construct a IBM Quantum Experience circuit for the following state transformation?

Please help me in building IBM Quantum Experience circuit for: $$ M|0\rangle = \frac{1}{2}(|0\rangle+|1\rangle+|2\rangle+|3\rangle) $$ Edit: Is it possible to make a circuit for a general ...
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Generate the state $\frac{-|0\rangle + |1\rangle}{\sqrt{2}}$ with qiskit: problem with Pauli-Z behavior

I want to construct the following state of a qubit using a quantum circuit: $\frac{-|0\rangle + |1\rangle}{\sqrt{2}}$ When I use the following qiskit code in Python: ...
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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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What is the |+⟩ and |-⟩ state?

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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Why is implementation of controlled Hadamard on IBM Q so complex?

With reference to question how to implement CCH gate I easily realized that CH gate can be implemented with $\mathrm{Ry}$ gates and $\mathrm{CNOT}$ followingly: Note $\theta = \frac{\pi}{4}$ for ...
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Why is a Hadamard gate unitary?

The Hadamard gate is a unitary gate, but how does the matrix times its own conjugate transpose actually result in the $I$ matrix? I am currently looking at it as a scalar, 0.707..., multiplied by the ...
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Why do multi-bit hadamards expands to what they do?

I'm a Computer Scientist undergrad student studying for an exam in Quantum computing. In all of the algorithms I have been studying (Deutsch–Jozsa, Simons, Shors, Grovers) I constantly see multi-qubit ...
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Is quantum superposition state a truth or an assumption?

Please, be patient with my question I already read that there is a heuristic that makes superposition a fact of reality. In addition, this superposition, when observed, it has a state of 0 or 1. ...
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What is the matrix representation for $n$-qubit gates?

Let's say I have more than one qbits $|0\rangle|1\rangle$ and I want to perform a $H$ on both of them. I know the matrix representation for the Hadamard on a single qbit is $$\frac{1}{\sqrt{2}}\begin{...
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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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Could the Hadamard gate have been constructed differently with similar characteristics?

Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$. $$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$ $$H^1 = \begin{bmatrix}-1&1\\1&...
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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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Analysis of the second Hadamard in the Detusch-Josza Algorithm

Consider the Deutsch-Josza, 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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Prove by induction $H^{\otimes n} \left| 0 \right>^{\otimes n} = \frac{1}{\sqrt{2^n}} \sum_{i=0}^{2^n -1} \left| i \right>$

Let H be the Hadamard operator. $$ H = (\left| 0 \right> \left< 0 \right| + \left| 0 \right> \left< 1 \right| + \left| 1 \right> \left< 0 \right| -\left| 1 \right> \left< 1 \...
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How do 2 Hadamard gates act on a single qubit?

When I perform $2$ Hadamard $H$ gates on a single qubit, why is the probability of getting $0$ as the outcome 100%? Why is it not 50% 0 and 50% 1 instead? Why is the second $H$ gate not putting the ...
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How to understand a phase operation between 2 Hadamard gates?

I would like to understand this image, of a "payload preparation" gate. A single H gate will create a superposition, while the phase will rotate 45 degrees. What does the second H gate do in this ...
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Finding a global phase that transform the Hadamard gate to an element of $SU(2)$ and propose an evoultion operator which implents the operation

I was looking back over an old assignment and I came across a question I wasn't quite sure how to do the problem statement is as follows: The Hadamard rotation is an element of the group $U(2)$. (i)...
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Projecting $\lvert ++ \rangle$ on Bell Basis

I understand that, projecting $\lvert 00\rangle$ on the Bell states would produce $\lvert\Phi^+\rangle$. Because, $$ CNOT(H\lvert0\rangle \otimes \lvert0\rangle) = \frac{1}{\sqrt{2}}(\lvert00\rangle +...