We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
Round durations in `GenericBackendV2`
<!--
⚠️ If you do not respect this template, your pull request will be closed.
⚠️ Your pull request title should be short detailed and understandable for all.
⚠️ Also, please add a release note file using reno if the change needs to be
  documented in the release notes.
⚠️ If your pull request fixes an open issue, please link to the issue.

- [ ] I have added the tests to cover my changes.
- [ ] I have updated the documentation accordingly.
- [ ] I have read the CONTRIBUTING document.
-->

### Summary
This PR makes sure that the conversion of `GenericBackendV2` instruction durations to `dt` is exact to avoid user warnings during scheduling of type:

`UserWarning: Duration is rounded to 616 [dt] = 1.367520e-07 [s] from 1.366887e-07 [s]`

Given that the durations are sampled randomly, and the rounded duration is the one used in the scheduling passes, we might as well make sure in advance that the conversion from seconds to dt will be exact and doesn't raise warnings.

### Details and comments
I am not sure this qualifies as a bugfix but I think it improves the readability of the test logs. For example, for `test_scheduling_backend_v2` in `test/python/compiler/test_transpiler.py`. Before:

```
/Users/ept/qiskit_workspace/qiskit/qiskit/circuit/duration.py:37: UserWarning: Duration is rounded to 986 [dt] = 2.188920e-07 [s] from 2.189841e-07 [s]
  warnings.warn(
/Users/ept/qiskit_workspace/qiskit/qiskit/circuit/duration.py:37: UserWarning: Duration is rounded to 2740 [dt] = 6.082800e-07 [s] from 6.083383e-07 [s]
  warnings.warn(
/Users/ept/qiskit_workspace/qiskit/qiskit/circuit/duration.py:37: UserWarning: Duration is rounded to 2697 [dt] = 5.987340e-07 [s] from 5.988312e-07 [s]
  warnings.warn(
/Users/ept/qiskit_workspace/qiskit/qiskit/circuit/duration.py:37: UserWarning: Duration is rounded to 178 [dt] = 3.951600e-08 [s] from 3.956636e-08 [s]
  warnings.warn(
.
----------------------------------------------------------------------
Ran 1 test in 0.548s

OK
```

After:

```
.
----------------------------------------------------------------------
Ran 1 test in 0.506s

OK
```


--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `qiskit/circuit/duration.py`
Content:
```
1 # This code is part of Qiskit.
2 #
3 # (C) Copyright IBM 2020.
4 #
5 # This code is licensed under the Apache License, Version 2.0. You may
6 # obtain a copy of this license in the LICENSE.txt file in the root directory
7 # of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
8 #
9 # Any modifications or derivative works of this code must retain this
10 # copyright notice, and modified files need to carry a notice indicating
11 # that they have been altered from the originals.
12 
13 """
14 Utilities for handling duration of a circuit instruction.
15 """
16 import warnings
17 
18 from qiskit.circuit import QuantumCircuit
19 from qiskit.circuit.exceptions import CircuitError
20 from qiskit.utils.units import apply_prefix
21 
22 
23 def duration_in_dt(duration_in_sec: float, dt_in_sec: float) -> int:
24     """
25     Return duration in dt.
26 
27     Args:
28         duration_in_sec: duration [s] to be converted.
29         dt_in_sec: duration of dt in seconds used for conversion.
30 
31     Returns:
32         Duration in dt.
33     """
34     res = round(duration_in_sec / dt_in_sec)
35     rounding_error = abs(duration_in_sec - res * dt_in_sec)
36     if rounding_error > 1e-15:
37         warnings.warn(
38             "Duration is rounded to %d [dt] = %e [s] from %e [s]"
39             % (res, res * dt_in_sec, duration_in_sec),
40             UserWarning,
41         )
42     return res
43 
44 
45 def convert_durations_to_dt(qc: QuantumCircuit, dt_in_sec: float, inplace=True):
46     """Convert all the durations in SI (seconds) into those in dt.
47 
48     Returns a new circuit if `inplace=False`.
49 
50     Parameters:
51         qc (QuantumCircuit): Duration of dt in seconds used for conversion.
52         dt_in_sec (float): Duration of dt in seconds used for conversion.
53         inplace (bool): All durations are converted inplace or return new circuit.
54 
55     Returns:
56         QuantumCircuit: Converted circuit if `inplace = False`, otherwise None.
57 
58     Raises:
59         CircuitError: if fail to convert durations.
60     """
61     if inplace:
62         circ = qc
63     else:
64         circ = qc.copy()
65 
66     for instruction in circ.data:
67         operation = instruction.operation
68         if operation.unit == "dt" or operation.duration is None:
69             continue
70 
71         if not operation.unit.endswith("s"):
72             raise CircuitError(f"Invalid time unit: '{operation.unit}'")
73 
74         duration = operation.duration
75         if operation.unit != "s":
76             duration = apply_prefix(duration, operation.unit)
77 
78         operation.duration = duration_in_dt(duration, dt_in_sec)
79         operation.unit = "dt"
80 
81     if circ.duration is not None:
82         circ.duration = duration_in_dt(circ.duration, dt_in_sec)
83         circ.unit = "dt"
84 
85     if not inplace:
86         return circ
87     else:
88         return None
89
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/qiskit/circuit/duration.py b/qiskit/circuit/duration.py
--- a/qiskit/circuit/duration.py
+++ b/qiskit/circuit/duration.py
@@ -78,8 +78,15 @@
         operation.duration = duration_in_dt(duration, dt_in_sec)
         operation.unit = "dt"
 
-    if circ.duration is not None:
-        circ.duration = duration_in_dt(circ.duration, dt_in_sec)
+    if circ.duration is not None and circ.unit != "dt":
+        if not circ.unit.endswith("s"):
+            raise CircuitError(f"Invalid time unit: '{circ.unit}'")
+
+        duration = circ.duration
+        if circ.unit != "s":
+            duration = apply_prefix(duration, circ.unit)
+
+        circ.duration = duration_in_dt(duration, dt_in_sec)
         circ.unit = "dt"
 
     if not inplace:

{"golden_diff": "diff --git a/qiskit/circuit/duration.py b/qiskit/circuit/duration.py\n--- a/qiskit/circuit/duration.py\n+++ b/qiskit/circuit/duration.py\n@@ -78,8 +78,15 @@\n         operation.duration = duration_in_dt(duration, dt_in_sec)\n         operation.unit = \"dt\"\n \n-    if circ.duration is not None:\n-        circ.duration = duration_in_dt(circ.duration, dt_in_sec)\n+    if circ.duration is not None and circ.unit != \"dt\":\n+        if not circ.unit.endswith(\"s\"):\n+            raise CircuitError(f\"Invalid time unit: '{circ.unit}'\")\n+\n+        duration = circ.duration\n+        if circ.unit != \"s\":\n+            duration = apply_prefix(duration, circ.unit)\n+\n+        circ.duration = duration_in_dt(duration, dt_in_sec)\n         circ.unit = \"dt\"\n \n     if not inplace:\n", "issue": "Round durations in `GenericBackendV2`\n<!--\r\n\u26a0\ufe0f If you do not respect this template, your pull request will be closed.\r\n\u26a0\ufe0f Your pull request title should be short detailed and understandable for all.\r\n\u26a0\ufe0f Also, please add a release note file using reno if the change needs to be\r\n  documented in the release notes.\r\n\u26a0\ufe0f If your pull request fixes an open issue, please link to the issue.\r\n\r\n- [ ] I have added the tests to cover my changes.\r\n- [ ] I have updated the documentation accordingly.\r\n- [ ] I have read the CONTRIBUTING document.\r\n-->\r\n\r\n### Summary\r\nThis PR makes sure that the conversion of `GenericBackendV2` instruction durations to `dt` is exact to avoid user warnings during scheduling of type:\r\n\r\n`UserWarning: Duration is rounded to 616 [dt] = 1.367520e-07 [s] from 1.366887e-07 [s]`\r\n\r\nGiven that the durations are sampled randomly, and the rounded duration is the one used in the scheduling passes, we might as well make sure in advance that the conversion from seconds to dt will be exact and doesn't raise warnings.\r\n\r\n### Details and comments\r\nI am not sure this qualifies as a bugfix but I think it improves the readability of the test logs. For example, for `test_scheduling_backend_v2` in `test/python/compiler/test_transpiler.py`. Before:\r\n\r\n```\r\n/Users/ept/qiskit_workspace/qiskit/qiskit/circuit/duration.py:37: UserWarning: Duration is rounded to 986 [dt] = 2.188920e-07 [s] from 2.189841e-07 [s]\r\n  warnings.warn(\r\n/Users/ept/qiskit_workspace/qiskit/qiskit/circuit/duration.py:37: UserWarning: Duration is rounded to 2740 [dt] = 6.082800e-07 [s] from 6.083383e-07 [s]\r\n  warnings.warn(\r\n/Users/ept/qiskit_workspace/qiskit/qiskit/circuit/duration.py:37: UserWarning: Duration is rounded to 2697 [dt] = 5.987340e-07 [s] from 5.988312e-07 [s]\r\n  warnings.warn(\r\n/Users/ept/qiskit_workspace/qiskit/qiskit/circuit/duration.py:37: UserWarning: Duration is rounded to 178 [dt] = 3.951600e-08 [s] from 3.956636e-08 [s]\r\n  warnings.warn(\r\n.\r\n----------------------------------------------------------------------\r\nRan 1 test in 0.548s\r\n\r\nOK\r\n```\r\n\r\nAfter:\r\n\r\n```\r\n.\r\n----------------------------------------------------------------------\r\nRan 1 test in 0.506s\r\n\r\nOK\r\n```\r\n\n", "before_files": [{"content": "# This code is part of Qiskit.\n#\n# (C) Copyright IBM 2020.\n#\n# This code is licensed under the Apache License, Version 2.0. You may\n# obtain a copy of this license in the LICENSE.txt file in the root directory\n# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.\n#\n# Any modifications or derivative works of this code must retain this\n# copyright notice, and modified files need to carry a notice indicating\n# that they have been altered from the originals.\n\n\"\"\"\nUtilities for handling duration of a circuit instruction.\n\"\"\"\nimport warnings\n\nfrom qiskit.circuit import QuantumCircuit\nfrom qiskit.circuit.exceptions import CircuitError\nfrom qiskit.utils.units import apply_prefix\n\n\ndef duration_in_dt(duration_in_sec: float, dt_in_sec: float) -> int:\n    \"\"\"\n    Return duration in dt.\n\n    Args:\n        duration_in_sec: duration [s] to be converted.\n        dt_in_sec: duration of dt in seconds used for conversion.\n\n    Returns:\n        Duration in dt.\n    \"\"\"\n    res = round(duration_in_sec / dt_in_sec)\n    rounding_error = abs(duration_in_sec - res * dt_in_sec)\n    if rounding_error > 1e-15:\n        warnings.warn(\n            \"Duration is rounded to %d [dt] = %e [s] from %e [s]\"\n            % (res, res * dt_in_sec, duration_in_sec),\n            UserWarning,\n        )\n    return res\n\n\ndef convert_durations_to_dt(qc: QuantumCircuit, dt_in_sec: float, inplace=True):\n    \"\"\"Convert all the durations in SI (seconds) into those in dt.\n\n    Returns a new circuit if `inplace=False`.\n\n    Parameters:\n        qc (QuantumCircuit): Duration of dt in seconds used for conversion.\n        dt_in_sec (float): Duration of dt in seconds used for conversion.\n        inplace (bool): All durations are converted inplace or return new circuit.\n\n    Returns:\n        QuantumCircuit: Converted circuit if `inplace = False`, otherwise None.\n\n    Raises:\n        CircuitError: if fail to convert durations.\n    \"\"\"\n    if inplace:\n        circ = qc\n    else:\n        circ = qc.copy()\n\n    for instruction in circ.data:\n        operation = instruction.operation\n        if operation.unit == \"dt\" or operation.duration is None:\n            continue\n\n        if not operation.unit.endswith(\"s\"):\n            raise CircuitError(f\"Invalid time unit: '{operation.unit}'\")\n\n        duration = operation.duration\n        if operation.unit != \"s\":\n            duration = apply_prefix(duration, operation.unit)\n\n        operation.duration = duration_in_dt(duration, dt_in_sec)\n        operation.unit = \"dt\"\n\n    if circ.duration is not None:\n        circ.duration = duration_in_dt(circ.duration, dt_in_sec)\n        circ.unit = \"dt\"\n\n    if not inplace:\n        return circ\n    else:\n        return None\n", "path": "qiskit/circuit/duration.py"}], "after_files": [{"content": "# This code is part of Qiskit.\n#\n# (C) Copyright IBM 2020.\n#\n# This code is licensed under the Apache License, Version 2.0. You may\n# obtain a copy of this license in the LICENSE.txt file in the root directory\n# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.\n#\n# Any modifications or derivative works of this code must retain this\n# copyright notice, and modified files need to carry a notice indicating\n# that they have been altered from the originals.\n\n\"\"\"\nUtilities for handling duration of a circuit instruction.\n\"\"\"\nimport warnings\n\nfrom qiskit.circuit import QuantumCircuit\nfrom qiskit.circuit.exceptions import CircuitError\nfrom qiskit.utils.units import apply_prefix\n\n\ndef duration_in_dt(duration_in_sec: float, dt_in_sec: float) -> int:\n    \"\"\"\n    Return duration in dt.\n\n    Args:\n        duration_in_sec: duration [s] to be converted.\n        dt_in_sec: duration of dt in seconds used for conversion.\n\n    Returns:\n        Duration in dt.\n    \"\"\"\n    res = round(duration_in_sec / dt_in_sec)\n    rounding_error = abs(duration_in_sec - res * dt_in_sec)\n    if rounding_error > 1e-15:\n        warnings.warn(\n            \"Duration is rounded to %d [dt] = %e [s] from %e [s]\"\n            % (res, res * dt_in_sec, duration_in_sec),\n            UserWarning,\n        )\n    return res\n\n\ndef convert_durations_to_dt(qc: QuantumCircuit, dt_in_sec: float, inplace=True):\n    \"\"\"Convert all the durations in SI (seconds) into those in dt.\n\n    Returns a new circuit if `inplace=False`.\n\n    Parameters:\n        qc (QuantumCircuit): Duration of dt in seconds used for conversion.\n        dt_in_sec (float): Duration of dt in seconds used for conversion.\n        inplace (bool): All durations are converted inplace or return new circuit.\n\n    Returns:\n        QuantumCircuit: Converted circuit if `inplace = False`, otherwise None.\n\n    Raises:\n        CircuitError: if fail to convert durations.\n    \"\"\"\n    if inplace:\n        circ = qc\n    else:\n        circ = qc.copy()\n\n    for instruction in circ.data:\n        operation = instruction.operation\n        if operation.unit == \"dt\" or operation.duration is None:\n            continue\n\n        if not operation.unit.endswith(\"s\"):\n            raise CircuitError(f\"Invalid time unit: '{operation.unit}'\")\n\n        duration = operation.duration\n        if operation.unit != \"s\":\n            duration = apply_prefix(duration, operation.unit)\n\n        operation.duration = duration_in_dt(duration, dt_in_sec)\n        operation.unit = \"dt\"\n\n    if circ.duration is not None and circ.unit != \"dt\":\n        if not circ.unit.endswith(\"s\"):\n            raise CircuitError(f\"Invalid time unit: '{circ.unit}'\")\n\n        duration = circ.duration\n        if circ.unit != \"s\":\n            duration = apply_prefix(duration, circ.unit)\n\n        circ.duration = duration_in_dt(duration, dt_in_sec)\n        circ.unit = \"dt\"\n\n    if not inplace:\n        return circ\n    else:\n        return None\n", "path": "qiskit/circuit/duration.py"}]}