Better decomposition of SWAP into ISWAP ** 0.5 (#2682)

* Better decomposition of SWAP into ISWAP ** 0.5

- Shortens length from 13 moments to 7 moments.
- Decomposition courtesy of @john6060 via @mpharrigan .

Fixes #2635

Author: dstrain115

cirq/google/optimizers/convert_to_sqrt_iswap.py

@@ -262,6 +262,21 @@ def swap_to_sqrt_iswap(a, b, turns):
             theta: The rotational angle that specifies the gate, where
             c = cos(π·t/2), s = sin(π·t/2), g = exp(i·π·t/2).
     """
+    if not isinstance(turns, sympy.Basic) and _near_mod_n(turns, 1.0, 2):
+        # Decomposition for cirq.SWAP
+        yield ops.Y(a)**0.5
+        yield ops.Y(b)**0.5
+        yield SQRT_ISWAP(a, b)
+        yield ops.Y(a)**-0.5
+        yield ops.Y(b)**-0.5
+        yield SQRT_ISWAP(a, b)
+        yield ops.X(a)**-0.5
+        yield ops.X(b)**-0.5
+        yield SQRT_ISWAP(a, b)
+        yield ops.X(a)**0.5
+        yield ops.X(b)**0.5
+        return
+
     yield ops.Z(a)**1.25
     yield ops.Z(b)**-0.25
     yield ops.ISWAP(a, b)**-0.5

cirq/google/optimizers/convert_to_sqrt_iswap_test.py

@@ -22,7 +22,7 @@ def _unitaries_allclose(circuit1, circuit2):
     [
         (cast(cirq.Gate, cirq.ISWAP), 7),  # cast is for fixing mypy confusion
         (cirq.CZ, 8),
-        (cirq.SWAP, 13),
+        (cirq.SWAP, 7),
         (cirq.CNOT, 9),
         (cirq.ISWAP**0.5, 1),
         (cirq.ISWAP**-0.5, 1),