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---
title: thermal_relaxation_error
description: API reference for qiskit.providers.aer.noise.thermal_relaxation_error
in_page_toc_min_heading_level: 1
python_api_type: function
python_api_name: qiskit.providers.aer.noise.thermal_relaxation_error
---
# qiskit.providers.aer.noise.thermal\_relaxation\_error
<Function id="qiskit.providers.aer.noise.thermal_relaxation_error" isDedicatedPage={true} github="https://github.com/qiskit/qiskit-aer/tree/stable/0.10/qiskit/providers/aer/noise/errors/standard_errors.py" signature="thermal_relaxation_error(t1, t2, time, excited_state_population=0)">
Return a single-qubit thermal relaxation quantum error channel.
**Parameters**
* **t1** (*double*) the $T_1$ relaxation time constant.
* **t2** (*double*) the $T_2$ relaxation time constant.
* **time** (*double*) the gate time for relaxation error.
* **excited\_state\_population** (*double*) the population of $|1\rangle$ state at equilibrium (default: 0).
**Returns**
a quantum error object for a noise model.
**Return type**
[QuantumError](qiskit.providers.aer.noise.QuantumError "qiskit.providers.aer.noise.QuantumError")
**Raises**
**NoiseError** If noise parameters are invalid.
## Additional information:
* For parameters to be valid $T_1$ and $T_2$ must satisfy $T_2 \le 2 T_1$.
* If $T_2 \le T_1$ the error can be expressed as a mixed reset and unitary error channel.
* If $T_1 < T_2 \le 2 T_1$ the error must be expressed as a general non-unitary Kraus error channel.
</Function>