# What is the concrete difference between qiskit thermal_relaxation_error and phase_amplitude_damping_error?

What is the concrete difference between those two error models in qiskit.providers.aer.noise?

For phase_amplitude_damping_error the Kraus operators are given explicitly in the documentation but not so for the thermal_relaxation_error. At least they both work towards the same equilibrium state. Physically they should have the same effect since a thermal relaxation is nothing but an amplitude damping and dephasing, correct?

The only difference I see is in the definition of the parameters. While phase_and_amplitude_damping_error has two separate parameters for the damping of amplitude and phase, T2 of thermal_relaxation_error includes both types as $$\frac{1}{T_2}=\frac{1}{T_2}+\frac{1}{T_p}$$ where $$T_1$$ describes amplitude damping and $$T_p$$ phase damping.

Are there further difference (also in the specific implementation) I have overlooked?

• I recommend look at test file from qiskit for understand how it been expected to be use.github.com/Qiskit/qiskit-aer/blob/… , github.com/Qiskit/qiskit-aer/blob/…
– poig
Jun 28 at 2:40
• These tests are nice to see, thank you. However, what I am looking for is not implemented ("line 39: # TODO: Test Kraus thermal relaxation error by comparing to amplitude damping channel"). Jun 29 at 14:58