Turn caching off by default when max_diff==1

doc/releases/changelog-dev.md

@@ -299,6 +299,9 @@
 
 <h3>Breaking changes 💔</h3>
 
+* Caching of executions is now turned off by default when `max_diff == 1`, as the classical overhead cost
+  outweighs the probability that duplicate circuits exists.
+
 * The entry point convention registering compilers with PennyLane has changed.
   [(#5140)](https://github.com/PennyLaneAI/pennylane/pull/5140)
 

pennylane/workflow/qnode.py

@@ -183,8 +183,9 @@ class QNode:
             Only applies if the device is queried for the gradient; gradient transform
             functions available in ``qml.gradients`` are only supported on the backward
             pass. The 'best' option chooses automatically between the two options and is default.
-        cache (bool or dict or Cache): Whether to cache evaluations. This can result in
-            a significant reduction in quantum evaluations during gradient computations.
+        cache=None (None or bool or dict or Cache): Whether to cache evalulations.
+            ``None`` indicates to cache only when ``max_diff > 1``. This can result in
+            a reduction in quantum evaluations during higher order gradient computations.
             If ``True``, a cache with corresponding ``cachesize`` is created for each batch
             execution. If ``False``, no caching is used. You may also pass your own cache
             to be used; this can be any object that implements the special methods
@@ -415,7 +416,7 @@ def __init__(
         expansion_strategy="gradient",
         max_expansion=10,
         grad_on_execution="best",
-        cache=True,
+        cache=None,
         cachesize=10000,
         max_diff=1,
         device_vjp=False,
@@ -483,6 +484,7 @@ def __init__(
         self.diff_method = diff_method
         self.expansion_strategy = expansion_strategy
         self.max_expansion = max_expansion
+        cache = (max_diff > 1) if cache is None else cache
 
         # execution keyword arguments
         self.execute_kwargs = {

tests/test_qnode.py

@@ -77,6 +77,26 @@ def test_copy():
     assert copied_qn.expansion_strategy == qn.expansion_strategy
 
 
+class TestInitialization:
+    def test_cache_initialization_maxdiff_1(self):
+        """Test that when max_diff = 1, the cache initializes to false."""
+
+        @qml.qnode(qml.device("default.qubit"), max_diff=1)
+        def f():
+            return qml.state()
+
+        assert f.execute_kwargs["cache"] is False
+
+    def test_cache_initialization_maxdiff_2(self):
+        """Test that when max_diff = 2, the cache initialization to True."""
+
+        @qml.qnode(qml.device("default.qubit"), max_diff=2)
+        def f():
+            return qml.state()
+
+        assert f.execute_kwargs["cache"] is True
+
+
 # pylint: disable=too-many-public-methods
 class TestValidation:
     """Tests for QNode creation and validation"""