Single qubit Hadamard gate transforms standard basis states (zero and one states) to their superpositions (plus and minus states)

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### Can you detect if the collapse of an entangled pair using a Hadamard gate?

I'm trying to understand how the Hadamard gate works with entangled pairs. If I have two particles A and B which are entangled and have gone through a Hadamard gate to become super-positioned Qubits, ...
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### Can we use Hadamard test to estimate phases?

There have been some questions discussing the Hadamard test and quantum phase estimation (QPE), but I did not find the answer to the following question. Suppose we are given $|\psi\rangle$, which is ...
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### How to apply the Hadamard gate to a given qubit state?

I have this qubit state: $$H \left[ \frac{1}{\sqrt{2}} |0\rangle + \left( \sqrt{\frac{2}{7}}+\frac{1}{\sqrt{7}}i \right) |1\rangle \right]$$ How to solve this given Hadamard gate on qubit? Hadamard ...
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Anyone of you can explain (with mathematical steps) me this circuit: I do not understand why the first qubit phase (as show on IBM composer) is influenced by the second. More precisely: In circuit ...
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### Why isn't $Ry(\pi/2)$ gate equivalent to Hadamard gate?

I've been experimenting with quantum circuits and can't quite fathom how the difference between states comes together. Speaking in terms of simulations using qiskit,...
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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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### 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?