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### Decomposition of a $4 \times 4$ unitary matrix

That paper appears to do their rotations in a very strange order. The method you're interested in is how to use Givens rotations to perform a QR decomposition (see, e.g. https://en.wikipedia.org/wiki/...

### Why is the operator $M_a |x\rangle= |a \cdot x \pmod{N} \rangle$ unitary?

Assuming $\gcd(N,a)=1$, then the operator $M_a$ mapping $x\in\mathbb Z_N$ to $a\cdot x \pmod N$ is a permutation, which means that it’s reversible, ergo unitary.
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### Question about Nielson & Chuang Problem 9.2

I have a sketch of ideas, but haven't buttoned up all the details into a proof so use it as a set of hints. Intuition: Kraus operators have a unitary freedom, thus you can get the next set of Kraus ...
1 vote

### Is qiskit.pulse.SamplePulse deprecated?

As per Qiskit release notes, SamplePulse has been deprecated in version 0.15 and removed in version 0.25. You should use Waveform...
1 vote

### Decomposition of a $4 \times 4$ unitary matrix

Note the following: if we have a vector with 2 entries $\begin{bmatrix} a \\ b \end{bmatrix}$, then we can use a unitary matrix to change the second entry to $0$. Namely, set $r = \sqrt{|a|^2 + |b|^2}$...
1 vote

### How to show that the GHZ state is absolutely maximally entangled?

I assume that you talk about the standard case of a $3$-qubit GHZ state (the generalized versions of $n$-qubit GHZ states are not absolutely maximally entangled):  |GHZ\rangle = \frac{1}{\sqrt{2}} \...

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