Improve QROM decomposition if no work wires provided (#6967)

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------------------------------------------------------------------------------------------------------------

**Context:**

Fix this bug [#6968]
[sc-84591]
**Description of the Change:**

Check if work wires are used and choose the correct decomposition based
on that.

**Benefits:**

More efficient decomposition

**Possible Drawbacks:**

**Related GitHub Issues:**

---------

Co-authored-by: Jay Soni <[email protected]>
Co-authored-by: Soran Jahangiri <[email protected]>

doc/releases/changelog-dev.md

@@ -431,10 +431,14 @@
   passed to the `QNode`, instead of assuming the method is always `deferred`.
   [(#6903)](https://github.com/PennyLaneAI/pennylane/pull/6903)
 
+* The `QROM` template is upgraded to decompose more efficiently when `work_wires` are not used.
+  [#6967)](https://github.com/PennyLaneAI/pennylane/pull/6967)
+
 <h3>Contributors ✍️</h3>
 
 This release contains contributions from (in alphabetical order):
 
+Guillermo Alonso,
 Utkarsh Azad,
 Henry Chang,
 Yushao Chen,

pennylane/templates/subroutines/qrom.py

@@ -246,7 +246,7 @@ def compute_decomposition(
                     )
                     swap_ops.insert(0, qml.ctrl(new_op, control=control_swap_wires[-ind - 1]))
 
-            if not clean:
+            if not clean or depth == 1:
                 # Based on this paper (Fig 1.c): https://arxiv.org/abs/1812.00954
                 decomp_ops = select_ops + swap_ops
 

tests/templates/test_subroutines/test_qrom.py

@@ -41,6 +41,20 @@ class TestQROM:
     @pytest.mark.parametrize(
         ("bitstrings", "target_wires", "control_wires", "work_wires", "clean"),
         [
+            (
+                ["111", "101", "100", "110"],
+                [0, 1, 2],
+                [3, 4],
+                None,
+                False,
+            ),
+            (
+                ["111", "101", "100", "110"],
+                [0, 1, 2],
+                [3, 4],
+                None,
+                True,
+            ),
             (
                 ["11", "01", "00", "10"],
                 [0, 1],
@@ -258,3 +272,14 @@ def test_wrong_wires_error(bitstrings, control_wires, target_wires, msg_match):
     """Test that error is raised if more ops are requested than can fit in control wires"""
     with pytest.raises(ValueError, match=msg_match):
         qml.QROM(bitstrings, control_wires, target_wires, work_wires=None)
+
+
+def test_none_work_wires_case():
+    """Test that clean version is not applied if work wires are not used"""
+
+    gates_clean = qml.QROM.compute_decomposition(["1", "0", "0", "1"], [0, 1], [2], [], clean=True)
+    expected_gates = qml.QROM.compute_decomposition(
+        ["1", "0", "0", "1"], [0, 1], [2], [], clean=False
+    )
+
+    assert gates_clean == expected_gates