From 58b86e1b8fe334fb6600e5c01d6aa818486ecfb9 Mon Sep 17 00:00:00 2001
From: Toshinari Itoko <15028342+itoko@users.noreply.github.com>
Date: Fri, 2 Dec 2022 12:24:23 +0900
Subject: [PATCH] Fix incorrect computation of excited state population (#1672)

This commits fixed a bug in NoiseModel.from_backend where using the temperature kwarg with
a non-default value would incorrectly compute the excited state population for the specified temperature.
Previously, there was an additional factor of 2 in the Boltzman distribution calculation leading to
an incorrect smaller value for the excited state population.

* Fix a bug in computation of excited population
* Improve reno
* Reword reno
---
 qiskit_aer/noise/device/models.py                  | 14 ++++++++------
 .../notes/fix-temperature-a9c51c4599af3a49.yaml    |  8 ++++++++
 2 files changed, 16 insertions(+), 6 deletions(-)
 create mode 100644 releasenotes/notes/fix-temperature-a9c51c4599af3a49.yaml

diff --git a/qiskit_aer/noise/device/models.py b/qiskit_aer/noise/device/models.py
index ad0b8ba836..ec67dc7d84 100644
--- a/qiskit_aer/noise/device/models.py
+++ b/qiskit_aer/noise/device/models.py
@@ -378,17 +378,19 @@ def _truncate_t2_value(t1, t2):
 
 
 def _excited_population(freq, temperature):
-    """Return excited state population"""
+    """Return excited state population from freq [GHz] and temperature [mK]."""
     population = 0
     if freq != inf and temperature != 0:
-        # Compute the excited state population from qubit
-        # frequency and temperature
-        # Boltzman constant  kB = 8.617333262-5 (eV/K)
+        # Compute the excited state population from qubit frequency and temperature
+        # based on Maxwell-Boltzmann distribution
+        # considering only qubit states (|0> and |1>), i.e. truncating higher energy states.
+        # Boltzman constant  kB = 8.617333262e-5 (eV/K)
         # Planck constant h = 4.135667696e-15 (eV.s)
         # qubit temperature temperatue = T (mK)
         # qubit frequency frequency = f (GHz)
-        # excited state population = 1/(1+exp((2*h*f*1e9)/(kb*T*1e-3)))
-        exp_param = exp((95.9849 * freq) / abs(temperature))
+        # excited state population = 1/(1+exp((h*f*1e9)/(kb*T*1e-3)))
+        # See e.g. Phys. Rev. Lett. 114, 240501 (2015).
+        exp_param = exp((47.99243 * freq) / abs(temperature))
         population = 1 / (1 + exp_param)
         if temperature < 0:
             # negative temperate implies |1> is thermal ground
diff --git a/releasenotes/notes/fix-temperature-a9c51c4599af3a49.yaml b/releasenotes/notes/fix-temperature-a9c51c4599af3a49.yaml
new file mode 100644
index 0000000000..b83388bfb0
--- /dev/null
+++ b/releasenotes/notes/fix-temperature-a9c51c4599af3a49.yaml
@@ -0,0 +1,8 @@
+---
+fixes:
+  - |
+    Fixed a bug in :meth:`NoiseModel.from_backend` where using the ``temperature`` kwarg with
+    a non-default value would incorrectly compute the excited state population for
+    the specified temperature. Previously, there was an additional factor of 2 in
+    the Boltzman distribution calculation leading to an incorrect smaller value
+    for the excited state population.