[BugFix] Fix powers of ISWAP and SISWAP (#7361)

**Context:**

**Description of the Change:**

**Benefits:**

**Possible Drawbacks:**

**Related GitHub Issues:**

Fixes #7359
[sc-90233]

---------

Co-authored-by: Yushao Chen (Jerry) <[email protected]>

Author: astralcai

doc/releases/changelog-dev.md

@@ -290,6 +290,8 @@
 * Fixed a bug where `two_qubit_decomposition` provides an incorrect decomposition for some special matrices.
   [(#7340)](https://github.com/PennyLaneAI/pennylane/pull/7340)
 
+* Fixes a bug where the powers of `qml.ISWAP` and `qml.SISWAP` were decomposed incorrectly.
+  [(#7361)](https://github.com/PennyLaneAI/pennylane/pull/7361)
 
 <h3>Contributors ✍️</h3>
 

pennylane/ops/qubit/non_parametric_ops.py

@@ -1788,10 +1788,12 @@ def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
         ]
 
     def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
-        z_mod2 = z % 2
-        if abs(z_mod2 - 0.5) < 1e-6:
+        z_mod4 = z % 4
+        if abs(z_mod4 - 0.5) < 1e-6:
             return [SISWAP(wires=self.wires)]
-        return super().pow(z_mod2)
+        if abs(z_mod4 - 2) < 1e-6:
+            return [qml.Z(wires=self.wires[0]), qml.Z(wires=self.wires[1])]
+        return super().pow(z_mod4)
 
 
 def _iswap_decomp_resources():
@@ -1962,8 +1964,12 @@ def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
         ]
 
     def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
-        z_mod4 = z % 4
-        return [ISWAP(wires=self.wires)] if z_mod4 == 2 else super().pow(z_mod4)
+        z_mod8 = z % 8
+        if abs(z_mod8 - 2) < 1e-6:
+            return [ISWAP(wires=self.wires)]
+        if abs(z_mod8 - 4) < 1e-6:
+            return [qml.Z(wires=self.wires[0]), qml.Z(wires=self.wires[1])]
+        return super().pow(z_mod8)
 
 
 def _siswap_decomp_resources():

tests/ops/qubit/test_non_parametric_ops.py

@@ -20,6 +20,7 @@
 
 import numpy as np
 import pytest
+import scipy as sp
 from gate_data import (
     CCZ,
     CH,
@@ -826,7 +827,6 @@ def test_repr(self):
     qml.PauliZ(0),
     qml.Hadamard("a"),
     qml.SWAP(wires=(0, 1)),
-    qml.ISWAP(wires=(0, 1)),
     qml.ECR(wires=(0, 1)),
     # Controlled operations
     qml.CNOT(wires=(0, 1)),
@@ -918,16 +918,37 @@ def test_pauliz_general_power(self, n):
         assert op_pow[0].__class__ is qml.PhaseShift
         assert qml.math.allclose(op_pow[0].data[0], np.pi * (n % 2))
 
-    @pytest.mark.parametrize("n", (0.5, 2.5, -1.5))
-    def test_ISWAP_sqaure_root(self, n):
-        """Test that SISWAP is the square root of ISWAP."""
-        op = qml.ISWAP(wires=(0, 1))
-
-        assert op.pow(n)[0].__class__ is qml.SISWAP
+    @pytest.mark.parametrize(
+        "n, expected",
+        [
+            (0, []),
+            (4, []),
+            (-4, []),
+            (-3, [qml.ISWAP(wires=(0, 1))]),
+            (5, [qml.ISWAP(wires=(0, 1))]),
+            (0.5, [qml.SISWAP(wires=(0, 1))]),
+            (4.5, [qml.SISWAP(wires=(0, 1))]),
+            (2, [qml.Z(0), qml.Z(1)]),
+            (-2, [qml.Z(0), qml.Z(1)]),
+            (6, [qml.Z(0), qml.Z(1)]),
+        ],
+    )
+    def test_ISWAP_powers(self, n, expected):
+        """Check that the special powers of ISWAP are correct."""
 
-        sqrt_mat = qml.matrix(op.pow, wire_order=[0, 1])(n)
-        sqrt_mat_squared = qml.math.linalg.matrix_power(sqrt_mat, 2)
-        assert qml.math.allclose(sqrt_mat_squared, qml.matrix(op))
+        op = qml.ISWAP(wires=(0, 1))
+        op_mat = qml.matrix(op)
+        pow_ops = op.pow(n)
+        assert pow_ops == expected
+        if not pow_ops:
+            pow_ops.append(qml.I(wires=(0, 1)))
+        mat = qml.matrix(qml.prod(*pow_ops), wire_order=[0, 1])
+        expected = (
+            qml.math.linalg.matrix_power(op_mat, n)
+            if isinstance(n, int)
+            else sp.linalg.fractional_matrix_power(op_mat, n)
+        )
+        assert qml.math.allclose(mat, expected)
 
     @pytest.mark.parametrize("offset", (0, 4, -4))
     def test_S_pow(self, offset):
@@ -971,17 +992,28 @@ def test_SX_pow(self, offset):
         with pytest.raises(qml.operation.PowUndefinedError):
             op.pow(2.43 + offset)
 
-    @pytest.mark.parametrize("offset", (0, 4, -4))
-    def test_SISWAP_pow(self, offset):
-        """Test powers of the SISWAP operator"""
-        op = qml.SISWAP(wires=("b", "c"))
-
-        assert len(op.pow(0 + offset)) == 0
-        assert op.pow(1 + offset)[0].__class__ is qml.SISWAP
-        assert op.pow(2 + offset)[0].__class__ is qml.ISWAP
+    @pytest.mark.parametrize(
+        "n, expected",
+        [
+            (0, []),
+            (8, []),
+            (9, [qml.SISWAP(wires=(0, 1))]),
+            (2, [qml.ISWAP(wires=(0, 1))]),
+            (4, [qml.Z(0), qml.Z(1)]),
+        ],
+    )
+    def test_SISWAP_powers(self, n, expected):
+        """Check that the special powers of SISWAP are correct."""
 
-        with pytest.raises(qml.operation.PowUndefinedError):
-            op.pow(2.34 + offset)
+        op = qml.SISWAP(wires=(0, 1))
+        op_mat = qml.matrix(op)
+        pow_ops = op.pow(n)
+        assert pow_ops == expected
+        if not pow_ops:
+            pow_ops.append(qml.I(wires=(0, 1)))
+        mat = qml.matrix(qml.prod(*pow_ops), wire_order=[0, 1])
+        expected = qml.math.linalg.matrix_power(op_mat, n)
+        assert qml.math.allclose(mat, expected)
 
     @pytest.mark.parametrize("op", (qml.WireCut(0), qml.Barrier(0)))
     @pytest.mark.parametrize("n", (2, 0.123, -2.3))