# Tag Info

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### Qiskit CNOT-gate matrix mixup?

Qiskit uses "little endian" bit ordering. That means, if A and B are $2 \times 2$ unitary matrices then $B \otimes A$ (note the order) is equivalent to applying $A$ to first qubit and $B$ to ...
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Accepted

### How do I create an inverse identity gate?

As a general rule, you wouldn't bother constructing this: it is just a global phase that has no observable consequence. If you really insist on doing this, introduce an ancilla qubit in the $|1\rangle$...

### How to create the state $\vert 0 \rangle+i \vert 1 \rangle$ using elementary gates?

Starting with the state $|\psi_0 \rangle = |0\rangle$, and we want to get to the state $|\psi_f \rangle = \dfrac{|0\rangle + i|1\rangle}{\sqrt{2}}$ then we must realize that we need to create some ...

### Can we write Pauli-Y gate without even complex part?

$\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} = i \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ There is no reason to factor out the $i$, it just make thing more cumbersome. I think ...
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### Can we write Pauli-Y gate without even complex part?

As noted by @KAJ226 in another answer, the global phase factor $i$ is unobservable and can be ignored, unless we are considering a controlled gate in which case the phase factor $i$ becomes a relative ...
Accepted

Accepted

### Shorthand notation for the sign flip gate

A unitary $U$ and $e^{i\phi}U$, which differs from it by a phase, act exact identically on any quantum state. Thus, they should really be considered the "same" unitary in terms of their action. ...

### Definition of the Pauli group and the Clifford group

The difference in definitions is from either taking the unitary group or the projective unitary group. That accounts for the constant prefactors of $\pm i$ that are missing. In lieu of a tikz ...

### How do I prove that the Hadamard satisfies $H\equiv e^{i\pi H/2}$?

For questions like this, the conventional physics notation is easier to work with than the QIT gate notation. Define $\vec \sigma = (\sigma_1,\sigma_2,\sigma_3)$ to represent the three Pauli matrices ...

### How to get specific state applying $e^{-i\phi \sigma_2/2}$ to $|0\rangle$ or $|1\rangle$?

A matrix function $f(A)$ for normal matrix $A$ is defined as follows \begin{equation} f(A)=\sum_{i=1}^{n}f(\lambda_i)v_iv_i^T \end{equation} where $\lambda_{i}$ is an eigenvalue and $v_{i}$ is ...
### How do I decompose the given $4\times 4$ matrix in terms of Pauli matrices?
From linear algebra, if $v_1, \dots, v_n$ is a basis of the vector space $V$ then every vector $v\in V$ can be written as a linear combination $$v = a_1 v_1 + \dots + a_n v_n\tag1$$ where the ...