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1

This is the color scheme for the phase factors supplied by IBM Q. It seems that it is not just the Y gate but any phase larger than pi is incorrectly color coded.


0

Gate $Y$ is described by matrix $$ Y= \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}. $$ When it acts on qubit in state $|0\rangle$, it returns state $\begin{pmatrix}0 \\i \end{pmatrix}$, i.e. a phase is $\pi/2$. When you do so on IBM Q a state [ 0+0j, 0+1j ] is returned as you can see in Visualization => State vector menu in IBM Q composer. For ...


6

What $\sigma^z_i$ means is that you've got a Pauli-$Z$ applied to qubit $i$, and nothing else on the other qubits (i.e. the identity). So, you could expand it as $$ I^{\otimes(i-1)}\otimes\sigma^z\otimes I^{n-i} $$ if your system has $n$ qubits. A term such as $\sigma^z_i\sigma^z_j$ is then a product of two of these, which is equivalent to the tensor product ...


2

$$R_y(\theta) = e^{-i\frac{\theta}{2}Y} = \begin{bmatrix} \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ \sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{bmatrix}$$ This gate might be named slightly differently depending on the source; Wikipedia doesn't seem to know it but this primer on rotations on Bloch sphere lists all rotation gates nicely.


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