Avoid lossing precision when scaling frequencies (#12392)

* Avoid lossing precision when scaling frequencies

Classes in pulse_instruction.py scale frequency values to GHz by
multipliying `ParameterExpression` with float 1e9. This can lead
to numerical errors on some systems using symengine. Instead, this
scaling can be done multiplying by integer 10**9.

See: #12359 (comment)

* Add release note

---------

Co-authored-by: Jake Lishman <jake.lishman@ibm.com>

qiskit/qobj/converters/pulse_instruction.py

@@ -234,7 +234,7 @@ def _convert_set_frequency(
             "name": "setf",
             "t0": time_offset + instruction.start_time,
             "ch": instruction.channel.name,
-            "frequency": instruction.frequency / 1e9,
+            "frequency": instruction.frequency / 10**9,
         }
         return self._qobj_model(**command_dict)
 
@@ -257,7 +257,7 @@ def _convert_shift_frequency(
             "name": "shiftf",
             "t0": time_offset + instruction.start_time,
             "ch": instruction.channel.name,
-            "frequency": instruction.frequency / 1e9,
+            "frequency": instruction.frequency / 10**9,
         }
         return self._qobj_model(**command_dict)
 
@@ -746,7 +746,7 @@ def _convert_setf(
         .. note::
 
             We assume frequency value is expressed in string with "GHz".
-            Operand value is thus scaled by a factor of 1e9.
+            Operand value is thus scaled by a factor of 10^9.
 
         Args:
             instruction: SetFrequency qobj instruction
@@ -755,7 +755,7 @@ def _convert_setf(
             Qiskit Pulse set frequency instructions
         """
         channel = self.get_channel(instruction.ch)
-        frequency = self.disassemble_value(instruction.frequency) * 1e9
+        frequency = self.disassemble_value(instruction.frequency) * 10**9
 
         yield instructions.SetFrequency(frequency, channel)
 
@@ -768,7 +768,7 @@ def _convert_shiftf(
         .. note::
 
             We assume frequency value is expressed in string with "GHz".
-            Operand value is thus scaled by a factor of 1e9.
+            Operand value is thus scaled by a factor of 10^9.
 
         Args:
             instruction: ShiftFrequency qobj instruction
@@ -777,7 +777,7 @@ def _convert_shiftf(
             Qiskit Pulse shift frequency schedule instructions
         """
         channel = self.get_channel(instruction.ch)
-        frequency = self.disassemble_value(instruction.frequency) * 1e9
+        frequency = self.disassemble_value(instruction.frequency) * 10**9
 
         yield instructions.ShiftFrequency(frequency, channel)
 

releasenotes/notes/fix-symbolic-unit-scaling-c3eb4d9be674dfd6.yaml

@@ -0,0 +1,8 @@
+---
+fixes:
+  - |
+    Fixed a floating-point imprecision when scaling certain pulse units
+    between seconds and nanoseconds.  If the pulse was symbolically defined,
+    an unnecessary floating-point error could be introduced by the scaling
+    for certain builds of ``symengine``, which could manifest in unexpected
+    results once the symbols were fully bound.  See `#12392 <https://github.com/Qiskit/qiskit/pull/12392>`__.