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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$H = e^{i\pi/4} \sqrt{iNOT}$?
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
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1answer
139 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....
3
votes
2answers
130 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, ...
1
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1answer
28 views
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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2answers
203 views
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 ...
3
votes
1answer
112 views
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:
...
5
votes
2answers
447 views
Why QFT can 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!!
0
votes
1answer
78 views
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. ...
2
votes
1answer
125 views
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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1answer
227 views
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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2answers
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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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2answers
140 views
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. ...
3
votes
2answers
66 views
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
$$\frac{1}{\sqrt{2}}\begin{...
6
votes
4answers
194 views
How do I prove that the Hadamard satisfies $H\equiv e^{i\pi H/2}$?
How can I demonstrate on the exponential part equality of the Hadamard matrix:
$$H=\frac{X+Z}{\sqrt2}\equiv\exp\left(i\frac{\pi}{2}\frac{X+Z}{\sqrt2}\right).$$
In general, how can I demonstrate on:
$\...
7
votes
2answers
372 views
Could the Hadamard gate have been constructed differently with similar characteristics?
Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$.
$$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$
$$H^1 = \begin{bmatrix}-1&1\\1&...
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vote
3answers
169 views
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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1answer
41 views
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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2answers
85 views
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.
$$ H = (\left| 0 \right> \left< 0 \right| + \left| 0 \right> \left< 1 \right| + \left| 1 \right> \left< 0 \right| -\left| 1 \right> \left< 1 \...
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3answers
359 views
How do 2 Hadamard gates act on a single qubit?
When I perform $2$ Hadamard $H$ gates on a single qubit, why is the probability of getting $0$ as the outcome 100%? Why is it not 50% 0 and 50% 1
instead?
Why is the second $H$ gate not putting the ...
6
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1answer
75 views
How to understand a phase operation between 2 Hadamard gates?
I would like to understand this image, of a "payload preparation" gate. A single H gate will create a superposition, while the phase will rotate 45 degrees. What does the second H gate do in this ...
5
votes
1answer
71 views
Finding a global phase that transform the Hadamard gate to an element of $SU(2)$ and propose an evoultion operator which implents the operation
I was looking back over an old assignment and I came across a question I wasn't quite sure how to do the problem statement is as follows:
The Hadamard rotation is an element of the group $U(2)$.
(i)...
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2answers
54 views
Projecting $\lvert ++ \rangle$ on Bell Basis
I understand that, projecting $\lvert 00\rangle$ on the Bell states would produce $\lvert\Phi^+\rangle$. Because,
$$
CNOT(H\lvert0\rangle \otimes \lvert0\rangle) = \frac{1}{\sqrt{2}}(\lvert00\rangle +...
