0
$\begingroup$

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?

$\endgroup$

1 Answer 1

1
$\begingroup$

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.
$\endgroup$
4
  • $\begingroup$ 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. $\endgroup$ 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
  • 1
    $\begingroup$ 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. $\endgroup$ Oct 28, 2021 at 13:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.