Nick Knows - Pauli Twirling

In this episode of Nick Knows, he considers “twirling” over a noisy quantum channel by the familiar Pauli operators: the I, X, Y, and Z gates. When done randomly, this method converts any noise channel to a “depolarizing” channel that is easier to characterize and mitigate (through averaging over experimental shots because it is stochastic).
References:

[dr-evil]

It's great that the description has links to various papers covering the topic.

[roncytron]

Unless I've missed something, the example given at 2:52 does not produce a CNOT gate, unless the gate in the middle is already a CNOT. If you solve for U in YZ*U*XY=CNOT, you obtain U=CNOT. So maybe you are describing twirling a CNOT using the Paul gates you placed around it. But if you were trying to replace CNOT with a different 2-qubit operation (the diagram is unclear), then you can implement CNOT by applying H to the bottom qubit, then control-Z to both qubits, then H on the bottom qubit again.

[Teucer]

This method of whiteboard with a light purple marker that isn't full of ink is an accessibility nightmare, even as someone with good vision its difficult to see whats on the board

[skk]

So, the objective of Pauli twirling is to do (noise) channel tomography? And then, based on the tomography result, we try to mitigate the error, right?

[mohsenmehrani]

Besides his wonderful instructions, I wonder if he writes horizontally-flipped or not. Thats gonna be super difficult for the speaker!