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

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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 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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### 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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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 $$\frac{1}{\sqrt{2}}\begin{... 4answers 334 views ### How do I prove that the Hadamard satisfies H\equiv e^{i\pi H/2}? How can I demonstrate on the exponential part equality of the Hadamard matrix:$$H=\frac{X+Z}{\sqrt2}\equiv\exp\left(i\frac{\pi}{2}\frac{X+Z}{\sqrt2}\right).$$In general, how can I demonstrate on: \... 2answers 449 views ### Could the Hadamard gate have been constructed differently with similar characteristics? Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it H^1.$$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}H^1 = \begin{bmatrix}-1&1\\1&...
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 ...