Add Willow gate (#7301)

* Add Willow gate

- On Willow processors, the parasitic c-phase parameter for iswap-like
gates has changed from the Sycamore processors.
- Update the parameter and add a new gate for simulation purposes.

* Change to pi/9

* Update cirq-google/cirq_google/ops/willow_gate.py

Co-authored-by: Pavol Juhas <pavol.juhas@gmail.com>

* format

* pi / 9

---------

Co-authored-by: Pavol Juhas <pavol.juhas@gmail.com>

Author: dstrain115

cirq-google/cirq_google/__init__.py

@@ -63,6 +63,8 @@
     PhysicalZTag as PhysicalZTag,
     SYC as SYC,
     SycamoreGate as SycamoreGate,
+    WILLOW as WILLOW,
+    WillowGate as WillowGate,
 )
 
 from cirq_google.transformers import (

cirq-google/cirq_google/json_resolver_cache.py

@@ -47,6 +47,7 @@ def _old_xmon(*args, **kwargs):
         'Coupler': cirq_google.Coupler,
         'GoogleNoiseProperties': cirq_google.GoogleNoiseProperties,
         'SycamoreGate': cirq_google.SycamoreGate,
+        'WillowGate': cirq_google.WillowGate,
         # cirq_google.GateTabulation has been removed and replaced by cirq.TwoQubitGateTabulation.
         'GateTabulation': TwoQubitGateTabulation,
         'PhysicalZTag': cirq_google.PhysicalZTag,

cirq-google/cirq_google/json_test_data/WILLOW.json

@@ -0,0 +1,3 @@
+{
+  "cirq_type": "WillowGate"
+}

cirq-google/cirq_google/json_test_data/WILLOW.repr

@@ -0,0 +1 @@
+cirq_google.WILLOW

cirq-google/cirq_google/json_test_data/WillowGate.json

@@ -0,0 +1,3 @@
+{
+  "cirq_type": "WillowGate"
+}

cirq-google/cirq_google/json_test_data/WillowGate.repr

@@ -0,0 +1 @@
+cirq_google.WILLOW

cirq-google/cirq_google/ops/__init__.py

@@ -33,3 +33,5 @@
 from cirq_google.ops.dynamical_decoupling_tag import (
     DynamicalDecouplingTag as DynamicalDecouplingTag,
 )
+
+from cirq_google.ops.willow_gate import WillowGate as WillowGate, WILLOW as WILLOW

cirq-google/cirq_google/ops/sycamore_gate.py

@@ -33,6 +33,12 @@ class SycamoreGate(cirq.FSimGate):
     is close to the gates that were used to demonstrate beyond
     classical resuts used in this paper:
     https://www.nature.com/articles/s41586-019-1666-5
+
+    Note that this gate will be transformed to a "ISWAP-like" gate
+    on hardware and that the C-phase value (phi) may change from
+    processor to processor.  In particular, if executed on newer
+    Willow processors, the phi value will be closer to π/9.
+    Use the Willow gate for simulation of this gate on newer devices.
     """
 
     def __init__(self):

cirq-google/cirq_google/ops/willow_gate.py

@@ -0,0 +1,72 @@
+# Copyright 2025 The Cirq Developers
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""An instance of FSimGate that works naturally on Google's Sycamore chip"""
+
+import numpy as np
+
+import cirq
+from cirq._doc import document
+
+
+class WillowGate(cirq.FSimGate):
+    """The Willow gate is a two-qubit gate equivalent to FSimGate(π/2, π/9).
+
+    The unitary of this gate is simulated as:
+
+        [[1, 0, 0, 0],
+         [0, 0, -1j, 0],
+         [0, -1j, 0, 0],
+         [0, 0, 0, exp(- 1j * π/9)]]
+
+    This gate can be performed on the Google's Willow chip.  Note that
+    this gate will be transformed to a "ISWAP-like" gate on hardware
+    and that the C-phase angle (phi) may change from processor to
+    processor.  The specified value is provided only for simulation
+    purposes.
+    """
+
+    def __init__(self):
+        super().__init__(theta=np.pi / 2, phi=np.pi / 9)
+
+    def __repr__(self) -> str:
+        return 'cirq_google.WILLOW'
+
+    def __str__(self) -> str:
+        return 'WILLOW'
+
+    def _circuit_diagram_info_(self, args: cirq.CircuitDiagramInfoArgs):
+        return 'WILLOW', 'WILLOW'
+
+    def _json_dict_(self):
+        return cirq.obj_to_dict_helper(self, [])
+
+
+WILLOW = WillowGate()
+document(
+    WILLOW,
+    """The Willow gate is a two-qubit gate equivalent to FSimGate(π/2, π/9).
+
+    The unitary of this gate is simulated as:
+
+        [[1, 0, 0, 0],
+         [0, 0, -1j, 0],
+         [0, -1j, 0, 0],
+         [0, 0, 0, exp(- 1j * π/9)]]
+
+    This gate can be performed on the Google's Willow chip.  Note that
+    this gate will be transformed to a "ISWAP-like" gate on hardware
+    and that the C-phase value (phi) may change from processor to
+    processor.  The specified value is provided only for simulation
+    purposes.""",
+)

cirq-google/cirq_google/ops/willow_gate_test.py

@@ -0,0 +1,62 @@
+# Copyright 2025 The Cirq Developers
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+import numpy as np
+
+import cirq
+import cirq_google as cg
+
+
+def test_consistent_protocols():
+    cirq.testing.assert_implements_consistent_protocols(
+        cg.WILLOW,
+        setup_code='import cirq\nimport numpy as np\nimport sympy\nimport cirq_google',
+        qubit_count=2,
+    )
+
+
+def test_willow_str_repr():
+    assert str(cg.WILLOW) == 'WILLOW'
+    assert repr(cg.WILLOW) == 'cirq_google.WILLOW'
+
+
+def test_willow_circuit_diagram():
+    a, b = cirq.LineQubit.range(2)
+    circuit = cirq.Circuit(cg.WILLOW(a, b))
+    cirq.testing.assert_has_diagram(
+        circuit,
+        """
+0: ───WILLOW───
+      │
+1: ───WILLOW───
+""",
+    )
+
+
+def test_willow_is_specific_fsim():
+    assert cg.WILLOW == cirq.FSimGate(theta=np.pi / 2, phi=np.pi / 9)
+
+
+def test_willow_unitary():
+    cirq.testing.assert_allclose_up_to_global_phase(
+        cirq.unitary(cg.WILLOW),
+        np.array(
+            [
+                [1.0, 0.0, 0.0, 0.0],
+                [0.0, 0.0, -1.0j, 0.0],
+                [0.0, -1.0j, 0.0, 0.0],
+                [0.0, 0.0, 0.0, np.exp(-1j * np.pi / 9)],
+            ]
+        ),
+        atol=1e-6,
+    )