Ensure bounded values for numpy binomial (#5447)

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**Context:** A
[user](https://discuss.pennylane.ai/t/multiple-resets-crash-spsaoptimizer-in-ver-0-35/4322/7)
reports errors when running MCM circuits, which fail due to
numpy-defined bounds checks in `qml.random.binomial` which should be
`0<= x <=1`. This error is due to the input data to `binomial` being
supplied with 1.0000000000000002 from another numpy layer, which
triggers this bounds check. This PR rounds towards 1.0 if an associated
ValueError is thrown.

**Description of the Change:** Adds a try-except block to catch and
round if the boundary check fails.

**Benefits:** Ensures continued use of MCM circuits.

**Possible Drawbacks:** Depending on the occurrence frequency of
boundary failures, replacing the try-except block may be better handled
by pre-validation against differences between unity and unity+macheps.

**Related GitHub Issues:**

doc/releases/changelog-dev.md

@@ -294,6 +294,9 @@
 
 <h3>Bug fixes 🐛</h3>
 
+* Avoid bounded value failures due to numerical noise with calls to `np.random.binomial`.
+  [(#5447)](https://github.com/PennyLaneAI/pennylane/pull/5447)
+
 * Using `@` with legacy Hamiltonian instances now properly de-queues the previously existing operations.
   [(#5454)](https://github.com/PennyLaneAI/pennylane/pull/5455)
 

pennylane/devices/qubit/apply_operation.py

@@ -265,7 +265,15 @@ def apply_mid_measure(
         return np.zeros_like(state)
     wire = op.wires
     probs = qml.devices.qubit.measure(qml.probs(wire), state)
-    sample = np.random.binomial(1, probs[1])
+
+    try:  # pragma: no cover
+        sample = np.random.binomial(1, probs[1])
+    except ValueError as e:  # pragma: no cover
+        if probs[1] > 1:  # MachEps error, safe to catch
+            sample = np.random.binomial(1, np.round(probs[1], 15))
+        else:  # Other general error, continue to fail
+            raise e
+
     mid_measurements[op] = sample
     if op.postselect is not None and sample != op.postselect:
         return np.zeros_like(state)