I am trying to simulate the logical error probability of color code under circuit-level noise.
In the code capacity noise and the phenomenological noise, the Pauli errors to the data qubits that occur with probability p are kept as a list (this is called actual error), and the information of the actual error is used to perform syndrome measurement, and the error is estimated by decoding from the obtained syndrome (this is called the estimated error). Then, the actual error and the estimated error are XORed, and if the resulting error is a logical operator, it is judged to be a logical error.
Now I want to calculate the logical error probability by the similar procedure with circuit-level noise. In this case, I understand the procedure for obtaining the estimated error, since it is almost the same as the phenomenological noise model, except that the syndrome measurement is performed by a syndrome measurement circuit. However, I do not know how to determine if the error correction by this estimated error results in a logical error. Is there a way to know actual errors in the same way as code capacity noise and the phenomenological noise? Also, I would like to know if there is a way to achieve this, especially in Stim.