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In Qiskit, there are many different Quantum Error Functions. From my understanding, pauli_error represents the error rate of $X, Y, Z$ independently, and deplolarizing_error is a combination of these Pauli operators. Is it correct? Are the two channels belong to incoherent errors?

Moreover, can phase_damping_error and amplitude_damping_error be regarded as $Z$ and $X$ errors respectively? Are they coherent or incoherent errors?

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I suggest to read the literature about these errors, they are not restricted to Qiskit. The textbook of Nielsen and Chuang has a very good chapter. In essence:

  • Pauli error: if you assign this error to some gate (e.g. Hadamard), and you attach probabilities (p_x, p_y, p_z) to it, then after that gate is simulated, with probability p_x, an X gate will run, with probability p_y, a Y gate will run, and with probability p_z, a Z gate will run. Note that it's not the error rate of the X gate etc.
  • Depolarizing: a special case of a Pauli error, where p_x = p_y = p_z.
  • Amplitude damping and phase damping are not X and Z and are incoherent.
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  • $\begingroup$ Thanks for your clarifying! To summarize my understanding, Pauli_error and Depolarizing are gate errors while amplitude_damping and phase_damping are thermal relaxation errors. Is that correct? $\endgroup$
    – peachnuts
    Oct 27, 2021 at 16:32
  • $\begingroup$ amplitude_damping and phase_damping are indeed thermal relaxation errors. I don't know what you mean by "gate errors", but Pauli_error and Depolarizing are unital. $\endgroup$
    – Yael Ben-Haim
    Oct 28, 2021 at 4:26
  • $\begingroup$ Thanks! The gate errors that we obtain from the calibration data, such as pauli-X, square root of X, CNOT errors, do they correspond to any specific type of errors included in the error functions, or they are a combination of all the errors? $\endgroup$
    – peachnuts
    Oct 28, 2021 at 8:02
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    $\begingroup$ They don't correspond to a specific error. There's a mathematical proof that, for Clifford gates, the different errors are averaged to depolarizing, and this fact is somehow more-or-less used when calculating gate errors, using interleaved randomized benchmarking. $\endgroup$
    – Yael Ben-Haim
    Oct 28, 2021 at 13:06

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