We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
MergeInteractions optimization is creating bad circuits
Not sure how this made it past the tests yet.

```python
def main():
    circuit = make_inefficient_circuit()
    print("BEFORE:")
    print(circuit.to_unitary_matrix().round(3))
    print()
    cirq.google.MergeInteractions().optimize_circuit(circuit)
    print("AFTER:")
    print(circuit.to_unitary_matrix().round(3))

def make_inefficient_circuit(t=0.1, v=0.11):
    from cirq import H, CNOT, Z
    a = cirq.NamedQubit('a')
    b = cirq.NamedQubit('b')

    return cirq.Circuit.from_ops(
        H(b),
        CNOT(a, b),
        H(b),
        CNOT(a, b),
        CNOT(b, a),
        H(a),
        CNOT(a, b),
        Z(a)**t, Z(b)**-t,
        CNOT(a, b),
        H(a), Z(b)**v,
        CNOT(a, b),
        Z(a)**-v, Z(b)**-v)
```

```
BEFORE:
[[ 1.   -0.j     0.   -0.j     0.   +0.j     0.   -0.j   ]
 [-0.   -0.j    -0.   -0.309j  0.951-0.j    -0.   +0.j   ]
 [ 0.   -0.j     0.951-0.j    -0.   -0.309j  0.   +0.j   ]
 [-0.   +0.j     0.   +0.j     0.   -0.j    -0.771+0.637j]]

AFTER:
[[-0.354-0.354j -0.354-0.354j -0.227-0.446j  0.227+0.446j]
 [-0.452-0.213j -0.452-0.213j  0.364+0.342j -0.364-0.342j]
 [-0.354-0.354j  0.354+0.354j -0.446-0.227j -0.446-0.227j]
 [-0.452-0.213j  0.452+0.213j  0.496+0.063j  0.496+0.063j]]
```

--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `cirq/google/merge_interactions.py`
Content:
```
1 # Copyright 2018 The Cirq Developers
2 #
3 # Licensed under the Apache License, Version 2.0 (the "License");
4 # you may not use this file except in compliance with the License.
5 # You may obtain a copy of the License at
6 #
7 #     https://www.apache.org/licenses/LICENSE-2.0
8 #
9 # Unless required by applicable law or agreed to in writing, software
10 # distributed under the License is distributed on an "AS IS" BASIS,
11 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 # See the License for the specific language governing permissions and
13 # limitations under the License.
14 
15 """An optimization pass that combines adjacent single-qubit rotations."""
16 
17 from typing import List, Tuple, Optional, cast
18 
19 import numpy as np
20 
21 from cirq import ops
22 from cirq.circuits import (
23     Circuit,
24     PointOptimizer,
25     PointOptimizationSummary,
26 )
27 from cirq.extension import Extensions
28 from cirq.google.decompositions import two_qubit_matrix_to_native_gates
29 
30 
31 class MergeInteractions(PointOptimizer):
32     """Combines adjacent constant single-qubit rotations."""
33 
34     def __init__(self,
35                  tolerance: float = 1e-8,
36                  allow_partial_czs: bool = True,
37                  extensions: Extensions = None) -> None:
38         self.tolerance = tolerance
39         self.allow_partial_czs = allow_partial_czs
40         self.extensions = extensions or Extensions()
41 
42     def optimization_at(self, circuit, index, op):
43         if len(op.qubits) != 2:
44             return None
45 
46         interaction_count, indices, matrix = (
47             self._scan_two_qubit_ops_into_matrix(circuit, index, op.qubits))
48         if interaction_count <= 1:
49             return None
50 
51         # Find a max-3-cz construction.
52         operations = two_qubit_matrix_to_native_gates(
53             op.qubits[0],
54             op.qubits[1],
55             matrix,
56             self.allow_partial_czs,
57             self.tolerance)
58 
59         # TODO: don't replace if there's no benefit in CZ depth.
60 
61         return PointOptimizationSummary(
62             clear_span=max(indices) + 1 - index,
63             clear_qubits=op.qubits,
64             new_operations=operations)
65 
66     def _op_to_matrix(self,
67                       op: ops.Operation,
68                       qubits: Tuple[ops.QubitId, ...]
69                       ) -> Optional[Tuple[np.ndarray, bool]]:
70         """Determines the effect of an operation on the given qubits.
71 
72         The operation must be a 1-qubit operation on one of the given qubits,
73         or a 2-qubit operation on both of the given qubits. Also, the operation
74         must have a known matrix. Otherwise None is returned.
75 
76         Args:
77             op: The operation to understand.
78             qubits: The qubits we care about. Order determines matrix tensor
79                 order.
80 
81         Returns:
82             None, or else a tuple containing a matrix equivalent to the effect
83             of the operation and a boolean indicating if the operation is a
84             2-qubit interaction.
85         """
86         q1, q2 = qubits
87 
88         known = self.extensions.try_cast(op.gate, ops.KnownMatrixGate)
89         if known is None:
90             return None
91         m = known.matrix()
92 
93         if op.qubits == qubits:
94             return m, True
95         if op.qubits == (q2, q1):
96             return MergeInteractions._flip_kron_order(m), True
97         if op.qubits == (q1,):
98             return np.kron(np.eye(2), m), False
99         if op.qubits == (q2,):
100             return np.kron(m, np.eye(2)), False
101 
102         return None
103 
104     def _scan_two_qubit_ops_into_matrix(
105             self,
106             circuit: Circuit,
107             index: Optional[int],
108             qubits: Tuple[ops.QubitId, ...]
109     ) -> Tuple[int, List[int], np.ndarray]:
110         """Accumulates operations affecting the given pair of qubits.
111 
112         The scan terminates when it hits the end of the circuit, finds an
113         operation without a known matrix, or finds an operation that interacts
114         the given qubits with other qubits.
115 
116         Args:
117             circuit: The circuit to scan for operations.
118             index: The index to start scanning forward from.
119             qubits: The pair of qubits we care about.
120 
121         Returns:
122             A tuple containing:
123                 0. The number of 2-qubit operations that were scanned.
124                 1. The moment indices those operations were on.
125                 2. A matrix equivalent to the effect of the scanned operations.
126         """
127 
128         product = np.eye(4, dtype=np.complex128)
129         interaction_count = 0
130         touched_indices = []
131 
132         while index is not None:
133             operations = {circuit.operation_at(q, index) for q in qubits}
134             op_data = [
135                 self._op_to_matrix(op, qubits)
136                 for op in operations
137                 if op
138             ]
139 
140             # Stop at any non-constant or non-local interaction.
141             if any(e is None for e in op_data):
142                 break
143             present_op_data = cast(List[Tuple[np.ndarray, bool]], op_data)
144 
145             for op_mat, interacts in present_op_data:
146                 product = np.dot(op_mat, product)
147                 if interacts:
148                     interaction_count += 1
149 
150             touched_indices.append(index)
151             index = circuit.next_moment_operating_on(qubits, index + 1)
152 
153         return interaction_count, touched_indices, product
154 
155     @staticmethod
156     def _flip_kron_order(mat4x4: np.ndarray) -> np.ndarray:
157         """Given M = sum(kron(a_i, b_i)), returns M' = sum(kron(b_i, a_i))."""
158         result = np.array([[0] * 4] * 4, dtype=np.complex128)
159         order = [0, 2, 1, 3]
160         for i in range(4):
161             for j in range(4):
162                 result[order[i], order[j]] = mat4x4[i, j]
163         return result
164
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/cirq/google/merge_interactions.py b/cirq/google/merge_interactions.py
--- a/cirq/google/merge_interactions.py
+++ b/cirq/google/merge_interactions.py
@@ -95,9 +95,9 @@
         if op.qubits == (q2, q1):
             return MergeInteractions._flip_kron_order(m), True
         if op.qubits == (q1,):
-            return np.kron(np.eye(2), m), False
-        if op.qubits == (q2,):
             return np.kron(m, np.eye(2)), False
+        if op.qubits == (q2,):
+            return np.kron(np.eye(2), m), False
 
         return None

{"golden_diff": "diff --git a/cirq/google/merge_interactions.py b/cirq/google/merge_interactions.py\n--- a/cirq/google/merge_interactions.py\n+++ b/cirq/google/merge_interactions.py\n@@ -95,9 +95,9 @@\n         if op.qubits == (q2, q1):\n             return MergeInteractions._flip_kron_order(m), True\n         if op.qubits == (q1,):\n-            return np.kron(np.eye(2), m), False\n-        if op.qubits == (q2,):\n             return np.kron(m, np.eye(2)), False\n+        if op.qubits == (q2,):\n+            return np.kron(np.eye(2), m), False\n \n         return None\n", "issue": "MergeInteractions optimization is creating bad circuits\nNot sure how this made it past the tests yet.\r\n\r\n```python\r\ndef main():\r\n    circuit = make_inefficient_circuit()\r\n    print(\"BEFORE:\")\r\n    print(circuit.to_unitary_matrix().round(3))\r\n    print()\r\n    cirq.google.MergeInteractions().optimize_circuit(circuit)\r\n    print(\"AFTER:\")\r\n    print(circuit.to_unitary_matrix().round(3))\r\n\r\ndef make_inefficient_circuit(t=0.1, v=0.11):\r\n    from cirq import H, CNOT, Z\r\n    a = cirq.NamedQubit('a')\r\n    b = cirq.NamedQubit('b')\r\n\r\n    return cirq.Circuit.from_ops(\r\n        H(b),\r\n        CNOT(a, b),\r\n        H(b),\r\n        CNOT(a, b),\r\n        CNOT(b, a),\r\n        H(a),\r\n        CNOT(a, b),\r\n        Z(a)**t, Z(b)**-t,\r\n        CNOT(a, b),\r\n        H(a), Z(b)**v,\r\n        CNOT(a, b),\r\n        Z(a)**-v, Z(b)**-v)\r\n```\r\n\r\n```\r\nBEFORE:\r\n[[ 1.   -0.j     0.   -0.j     0.   +0.j     0.   -0.j   ]\r\n [-0.   -0.j    -0.   -0.309j  0.951-0.j    -0.   +0.j   ]\r\n [ 0.   -0.j     0.951-0.j    -0.   -0.309j  0.   +0.j   ]\r\n [-0.   +0.j     0.   +0.j     0.   -0.j    -0.771+0.637j]]\r\n\r\nAFTER:\r\n[[-0.354-0.354j -0.354-0.354j -0.227-0.446j  0.227+0.446j]\r\n [-0.452-0.213j -0.452-0.213j  0.364+0.342j -0.364-0.342j]\r\n [-0.354-0.354j  0.354+0.354j -0.446-0.227j -0.446-0.227j]\r\n [-0.452-0.213j  0.452+0.213j  0.496+0.063j  0.496+0.063j]]\r\n```\n", "before_files": [{"content": "# Copyright 2018 The Cirq Developers\n#\n# Licensed under the Apache License, Version 2.0 (the \"License\");\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#     https://www.apache.org/licenses/LICENSE-2.0\n#\n# Unless required by applicable law or agreed to in writing, software\n# distributed under the License is distributed on an \"AS IS\" BASIS,\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n# limitations under the License.\n\n\"\"\"An optimization pass that combines adjacent single-qubit rotations.\"\"\"\n\nfrom typing import List, Tuple, Optional, cast\n\nimport numpy as np\n\nfrom cirq import ops\nfrom cirq.circuits import (\n    Circuit,\n    PointOptimizer,\n    PointOptimizationSummary,\n)\nfrom cirq.extension import Extensions\nfrom cirq.google.decompositions import two_qubit_matrix_to_native_gates\n\n\nclass MergeInteractions(PointOptimizer):\n    \"\"\"Combines adjacent constant single-qubit rotations.\"\"\"\n\n    def __init__(self,\n                 tolerance: float = 1e-8,\n                 allow_partial_czs: bool = True,\n                 extensions: Extensions = None) -> None:\n        self.tolerance = tolerance\n        self.allow_partial_czs = allow_partial_czs\n        self.extensions = extensions or Extensions()\n\n    def optimization_at(self, circuit, index, op):\n        if len(op.qubits) != 2:\n            return None\n\n        interaction_count, indices, matrix = (\n            self._scan_two_qubit_ops_into_matrix(circuit, index, op.qubits))\n        if interaction_count <= 1:\n            return None\n\n        # Find a max-3-cz construction.\n        operations = two_qubit_matrix_to_native_gates(\n            op.qubits[0],\n            op.qubits[1],\n            matrix,\n            self.allow_partial_czs,\n            self.tolerance)\n\n        # TODO: don't replace if there's no benefit in CZ depth.\n\n        return PointOptimizationSummary(\n            clear_span=max(indices) + 1 - index,\n            clear_qubits=op.qubits,\n            new_operations=operations)\n\n    def _op_to_matrix(self,\n                      op: ops.Operation,\n                      qubits: Tuple[ops.QubitId, ...]\n                      ) -> Optional[Tuple[np.ndarray, bool]]:\n        \"\"\"Determines the effect of an operation on the given qubits.\n\n        The operation must be a 1-qubit operation on one of the given qubits,\n        or a 2-qubit operation on both of the given qubits. Also, the operation\n        must have a known matrix. Otherwise None is returned.\n\n        Args:\n            op: The operation to understand.\n            qubits: The qubits we care about. Order determines matrix tensor\n                order.\n\n        Returns:\n            None, or else a tuple containing a matrix equivalent to the effect\n            of the operation and a boolean indicating if the operation is a\n            2-qubit interaction.\n        \"\"\"\n        q1, q2 = qubits\n\n        known = self.extensions.try_cast(op.gate, ops.KnownMatrixGate)\n        if known is None:\n            return None\n        m = known.matrix()\n\n        if op.qubits == qubits:\n            return m, True\n        if op.qubits == (q2, q1):\n            return MergeInteractions._flip_kron_order(m), True\n        if op.qubits == (q1,):\n            return np.kron(np.eye(2), m), False\n        if op.qubits == (q2,):\n            return np.kron(m, np.eye(2)), False\n\n        return None\n\n    def _scan_two_qubit_ops_into_matrix(\n            self,\n            circuit: Circuit,\n            index: Optional[int],\n            qubits: Tuple[ops.QubitId, ...]\n    ) -> Tuple[int, List[int], np.ndarray]:\n        \"\"\"Accumulates operations affecting the given pair of qubits.\n\n        The scan terminates when it hits the end of the circuit, finds an\n        operation without a known matrix, or finds an operation that interacts\n        the given qubits with other qubits.\n\n        Args:\n            circuit: The circuit to scan for operations.\n            index: The index to start scanning forward from.\n            qubits: The pair of qubits we care about.\n\n        Returns:\n            A tuple containing:\n                0. The number of 2-qubit operations that were scanned.\n                1. The moment indices those operations were on.\n                2. A matrix equivalent to the effect of the scanned operations.\n        \"\"\"\n\n        product = np.eye(4, dtype=np.complex128)\n        interaction_count = 0\n        touched_indices = []\n\n        while index is not None:\n            operations = {circuit.operation_at(q, index) for q in qubits}\n            op_data = [\n                self._op_to_matrix(op, qubits)\n                for op in operations\n                if op\n            ]\n\n            # Stop at any non-constant or non-local interaction.\n            if any(e is None for e in op_data):\n                break\n            present_op_data = cast(List[Tuple[np.ndarray, bool]], op_data)\n\n            for op_mat, interacts in present_op_data:\n                product = np.dot(op_mat, product)\n                if interacts:\n                    interaction_count += 1\n\n            touched_indices.append(index)\n            index = circuit.next_moment_operating_on(qubits, index + 1)\n\n        return interaction_count, touched_indices, product\n\n    @staticmethod\n    def _flip_kron_order(mat4x4: np.ndarray) -> np.ndarray:\n        \"\"\"Given M = sum(kron(a_i, b_i)), returns M' = sum(kron(b_i, a_i)).\"\"\"\n        result = np.array([[0] * 4] * 4, dtype=np.complex128)\n        order = [0, 2, 1, 3]\n        for i in range(4):\n            for j in range(4):\n                result[order[i], order[j]] = mat4x4[i, j]\n        return result\n", "path": "cirq/google/merge_interactions.py"}], "after_files": [{"content": "# Copyright 2018 The Cirq Developers\n#\n# Licensed under the Apache License, Version 2.0 (the \"License\");\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#     https://www.apache.org/licenses/LICENSE-2.0\n#\n# Unless required by applicable law or agreed to in writing, software\n# distributed under the License is distributed on an \"AS IS\" BASIS,\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n# limitations under the License.\n\n\"\"\"An optimization pass that combines adjacent single-qubit rotations.\"\"\"\n\nfrom typing import List, Tuple, Optional, cast\n\nimport numpy as np\n\nfrom cirq import ops\nfrom cirq.circuits import (\n    Circuit,\n    PointOptimizer,\n    PointOptimizationSummary,\n)\nfrom cirq.extension import Extensions\nfrom cirq.google.decompositions import two_qubit_matrix_to_native_gates\n\n\nclass MergeInteractions(PointOptimizer):\n    \"\"\"Combines adjacent constant single-qubit rotations.\"\"\"\n\n    def __init__(self,\n                 tolerance: float = 1e-8,\n                 allow_partial_czs: bool = True,\n                 extensions: Extensions = None) -> None:\n        self.tolerance = tolerance\n        self.allow_partial_czs = allow_partial_czs\n        self.extensions = extensions or Extensions()\n\n    def optimization_at(self, circuit, index, op):\n        if len(op.qubits) != 2:\n            return None\n\n        interaction_count, indices, matrix = (\n            self._scan_two_qubit_ops_into_matrix(circuit, index, op.qubits))\n        if interaction_count <= 1:\n            return None\n\n        # Find a max-3-cz construction.\n        operations = two_qubit_matrix_to_native_gates(\n            op.qubits[0],\n            op.qubits[1],\n            matrix,\n            self.allow_partial_czs,\n            self.tolerance)\n\n        # TODO: don't replace if there's no benefit in CZ depth.\n\n        return PointOptimizationSummary(\n            clear_span=max(indices) + 1 - index,\n            clear_qubits=op.qubits,\n            new_operations=operations)\n\n    def _op_to_matrix(self,\n                      op: ops.Operation,\n                      qubits: Tuple[ops.QubitId, ...]\n                      ) -> Optional[Tuple[np.ndarray, bool]]:\n        \"\"\"Determines the effect of an operation on the given qubits.\n\n        The operation must be a 1-qubit operation on one of the given qubits,\n        or a 2-qubit operation on both of the given qubits. Also, the operation\n        must have a known matrix. Otherwise None is returned.\n\n        Args:\n            op: The operation to understand.\n            qubits: The qubits we care about. Order determines matrix tensor\n                order.\n\n        Returns:\n            None, or else a tuple containing a matrix equivalent to the effect\n            of the operation and a boolean indicating if the operation is a\n            2-qubit interaction.\n        \"\"\"\n        q1, q2 = qubits\n\n        known = self.extensions.try_cast(op.gate, ops.KnownMatrixGate)\n        if known is None:\n            return None\n        m = known.matrix()\n\n        if op.qubits == qubits:\n            return m, True\n        if op.qubits == (q2, q1):\n            return MergeInteractions._flip_kron_order(m), True\n        if op.qubits == (q1,):\n            return np.kron(m, np.eye(2)), False\n        if op.qubits == (q2,):\n            return np.kron(np.eye(2), m), False\n\n        return None\n\n    def _scan_two_qubit_ops_into_matrix(\n            self,\n            circuit: Circuit,\n            index: Optional[int],\n            qubits: Tuple[ops.QubitId, ...]\n    ) -> Tuple[int, List[int], np.ndarray]:\n        \"\"\"Accumulates operations affecting the given pair of qubits.\n\n        The scan terminates when it hits the end of the circuit, finds an\n        operation without a known matrix, or finds an operation that interacts\n        the given qubits with other qubits.\n\n        Args:\n            circuit: The circuit to scan for operations.\n            index: The index to start scanning forward from.\n            qubits: The pair of qubits we care about.\n\n        Returns:\n            A tuple containing:\n                0. The number of 2-qubit operations that were scanned.\n                1. The moment indices those operations were on.\n                2. A matrix equivalent to the effect of the scanned operations.\n        \"\"\"\n\n        product = np.eye(4, dtype=np.complex128)\n        interaction_count = 0\n        touched_indices = []\n\n        while index is not None:\n            operations = {circuit.operation_at(q, index) for q in qubits}\n            op_data = [\n                self._op_to_matrix(op, qubits)\n                for op in operations\n                if op\n            ]\n\n            # Stop at any non-constant or non-local interaction.\n            if any(e is None for e in op_data):\n                break\n            present_op_data = cast(List[Tuple[np.ndarray, bool]], op_data)\n\n            for op_mat, interacts in present_op_data:\n                product = np.dot(op_mat, product)\n                if interacts:\n                    interaction_count += 1\n\n            touched_indices.append(index)\n            index = circuit.next_moment_operating_on(qubits, index + 1)\n\n        return interaction_count, touched_indices, product\n\n    @staticmethod\n    def _flip_kron_order(mat4x4: np.ndarray) -> np.ndarray:\n        \"\"\"Given M = sum(kron(a_i, b_i)), returns M' = sum(kron(b_i, a_i)).\"\"\"\n        result = np.array([[0] * 4] * 4, dtype=np.complex128)\n        order = [0, 2, 1, 3]\n        for i in range(4):\n            for j in range(4):\n                result[order[i], order[j]] = mat4x4[i, j]\n        return result\n", "path": "cirq/google/merge_interactions.py"}]}