I know there are various quantum noise channels, which include the depolarizing channel, the dephasing channel and the bit-flip channel; We can apply them in simulators easily.
However, is there any standard to choose the model we apply?
I mean, why we should (for instance) choose a flip channel over a depolarizing channel and when should we choose a specific channel? Why is the depolarizing channel commonly used?
Some thoughts:
From a theoretical perspective, the depolarizing channel is the 'standard' (if there is such a thing) or by some means the most applicable.
Because the Paulis (together with the identity operator) form a basis for $SU(2)$, if a code can correct the $X, Y$ and $Z$ flips on a certain qubit (and it it is able to correctly identify no error (i.e. '$I$-flip') having happened), it can correct all errors on that qubit. A theoretical analysis of a code cares a little less about the relative probabilities of these three flips happening, so we just as well can set them all to $\frac{p}{3}$, thereby obtaining the depolarizing channel.
The depolarizing channel $\Lambda_{\mathrm{depo}}$ can be written as:
$$ \Lambda_{\mathrm{deph}}\left(\begin{bmatrix}a & b \\ b^{*} & d\end{bmatrix}\right) = \begin{bmatrix} (1-\frac{2p}{3})a + \frac{2p}{3}d & (1-\frac{4p}{3}) b \\ (1-\frac{4p}{3})b^{*} & (1-\frac{2p}{3})d + \frac{2p}{3}a\end{bmatrix}. $$ Since $d = 1-a$, we can rewrite this to:
$$ \Lambda_{\mathrm{deph}}\left(\rho_{\mathrm{in}}\right) = (1-\frac{4p}{3})\rho_{\mathrm{in}} + \frac{4p}{3} \frac{I}{2}, $$ which is a convex combination of the input $\rho_{\mathrm{in}}$ and the maximally mixed state $\frac{I}{2}$. Furthermore, if you would equate $p$ to the elapsed time, $p$ would asymptotically go to $\frac{3}{4}$, thereby obtaining the maximally mixed state; therefore the depolarizing channel is in some way the 'worst' noise channel: it destroys both all quantum- (i.e. coherent superpositions) and classical information (there's literally only noise left) in the qubit.
If you want your simulation to be more true to the physical world, the depolarizing channel is not a very good model, as much as theorists might like it to be. A good first model for noise in qubits is the combination of two channels, the dephasing channel $\Lambda_{\mathrm{deph}}$ and the amplitude damping channel $\Lambda_{\mathrm{amp}}$.
Loosely speaking, the dephasing channel map destroys the coherent phase between the $|0\rangle$ and $|1\rangle$ state:
$$ \Lambda_{\mathrm{deph}}\left(\begin{bmatrix}a & b \\ b^{*} & 1-a\end{bmatrix}\right) = \begin{bmatrix}a & e^{-\frac{t}{T_{2}}} b \\ e^{-\frac{t}{T_{2}}}b^{*} & 1-a\end{bmatrix}, $$
where $T_{2}$ is known as the characteristic qubit dephasing time.
The Kraus operators of $\Lambda_{\mathrm{deph}}$ are $A_{1} = \sqrt{1-p}I$ and $A_{2} = \sqrt{p}Z$, so it is still a Pauli channel, which can help in the analysis or simulation.
$\Lambda_{\mathrm{amp}}$ is a little bit trickier: it simulates the relaxation of the excited (by convention $|1\rangle$) state, and maps it to the $|0\rangle$ state:
$$ \Lambda_{\mathrm{amp}}\left(\begin{bmatrix}a & b \\ b^{*} & 1-a\end{bmatrix}\right) = \begin{bmatrix}a & e^{-\frac{t}{2T_{1}}} b \\ e^{-\frac{t}{2T_{1}}} b^{*} & e^{-\frac{t}{T_{1}}}(1-a)\end{bmatrix}, $$ where $T_{1}$ is known as the qubit relaxation time.
The Kraus operators are also a little trickier: $B_{1} = \begin{bmatrix}1 & 0 \\ 0 & \sqrt{1-p}\end{bmatrix}$ and $B_{2} = \begin{bmatrix}0 & \sqrt{p} \\ 0 & 0\end{bmatrix}$. This means that amplitude damping channel is not a Pauli channel (allthough its Kraus operators can of course be written as linear combinations of the Paulis).
A simulation of a system undergoing both an amplitude damping and dephasing is a good start. There is one big caveat, however: this does not take leakage errors into account whatsoever. Depending on the physical system you are trying to simulate, this might range from either not a very large issue (e.g. for quantum dots) to a gross oversimplification (e.g. for transmon qubits).
