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 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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1answer
511 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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2answers
92 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” ...
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2answers
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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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2answers
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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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2answers
448 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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2answers
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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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1answer
139 views

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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3answers
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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 ...