# In Qiskit, add amplitude_damping_error to qubits in the circuit, how to know T1?

In Qiskit, add amplitude_damping_error to qubits in the circuit, how to know T1?

amplitude_damping_error(param_amp, excited_state_population=0, canonical_kraus=True)

What is the process of add amplitude_damping_error to a instruction of one qubit? What is the meaning of param_amp? How can I compute the T1 from param_amp or other parameters are needed?

Amplitude Damping Channel

When describing a quantum system undergoing energy dissipation because of some type of interaction with the environment, we apply a quantum operation known as amplitude damping. So, amplitude damping describes a decay process; a channel where the state $$|0\rangle$$ is transmitted faithfully but $$|1\rangle$$ (the excited state) is transmitted correctly with probability $$1-\gamma$$ and decays to $$|0\rangle$$ (the ground state) with probability $$\gamma$$ [1].

The parameter $$\gamma$$ is a time-dependent function, which is often characterized by $$1- e^{-t/T_1}$$, where $$t$$ is time and $$T_1$$ is the relaxation time.

Using amplitude_damping_error()

In Qiskit you add amplitude damping error to a one-qubit instruction as follows:

from qiskit_aer.noise import NoiseModel
from qiskit_aer.noise.errors.standard_errors import amplitude_damping_error
import numpy as np

# 1) Calculate param_amp (i.e., gamma)
T1 = 25.0
gate_time = 0.1
param_amp = 1 - np.exp(-gate_time / T1)

# 2) Define amplitude damping quantum error channel
error = amplitude_damping_error(param_amp)

# 3) Create the noise model and add the quantum error to it:
noise_model = NoiseModel()
# Or,

param_amp is the damping parameter for the amplitude damping channel.