Fix bitstring padding in the BackendSampler (Qiskit#9744)

* fix padding

* add reno

qiskit/primitives/backend_sampler.py

@@ -165,7 +165,7 @@ def _postprocessing(self, result: Result, circuits: list[QuantumCircuit]) -> Sam
         probabilities = []
         metadata: list[dict[str, Any]] = [{} for _ in range(len(circuits))]
         for count in counts:
-            prob_dist = {k: v / shots for k, v in count.int_outcomes().items()}
+            prob_dist = {k: v / shots for k, v in count.items()}
             probabilities.append(
                 QuasiDistribution(prob_dist, shots=shots, stddev_upper_bound=math.sqrt(1 / shots))
             )

releasenotes/notes/fix-backendsampler-padding-ed959e6dc3deb3f3.yaml

@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Fixed a bug in the :class:`.BackendSampler` where the binary probability bitstrings
+    were truncated to the minimal number of bits required to represent the largest outcome
+    as integer. That means that if e.g. ``{"0001": 1.0}`` was measured, the result was truncated
+    to ``{"1": 1.0}``.

test/python/primitives/test_backend_sampler.py

@@ -26,6 +26,7 @@
 from qiskit.primitives import BackendSampler, SamplerResult
 from qiskit.providers import JobStatus, JobV1
 from qiskit.providers.fake_provider import FakeNairobi, FakeNairobiV2
+from qiskit.providers.basicaer import QasmSimulatorPy
 from qiskit.test import QiskitTestCase
 from qiskit.transpiler import PassManager
 from qiskit.utils import optionals
@@ -361,6 +362,26 @@ def test_sequential_run(self):
         self.assertDictAlmostEqual(result3.quasi_dists[0], {0: 1}, 0.1)
         self.assertDictAlmostEqual(result3.quasi_dists[1], {1: 1}, 0.1)
 
+    def test_outcome_bitstring_size(self):
+        """Test that the result bitstrings are properly padded.
+
+        E.g. measuring '0001' should not get truncated to '1'.
+        """
+        qc = QuantumCircuit(4)
+        qc.x(0)
+        qc.measure_all()
+
+        # We need a noise-free backend here (shot noise is fine) to ensure that
+        # the only bit string measured is "0001". With device noise, it could happen that
+        # strings with a leading 1 are measured and then the truncation cannot be tested.
+        sampler = BackendSampler(backend=QasmSimulatorPy())
+
+        result = sampler.run(qc).result()
+        probs = result.quasi_dists[0].binary_probabilities()
+
+        self.assertIn("0001", probs.keys())
+        self.assertEqual(len(probs), 1)
+
     def test_bound_pass_manager(self):
         """Test bound pass manager."""