[4173] Add atol/rtol for unitary checks in MatrixGate (#4220)

Add rtol/atol for unitary checks in MatrixGate.

Fixes #4173.

cirq-core/cirq/ops/matrix_gates.py

@@ -29,7 +29,14 @@
 class MatrixGate(raw_types.Gate):
     """A unitary qubit or qudit gate defined entirely by its matrix."""
 
-    def __init__(self, matrix: np.ndarray, *, qid_shape: Optional[Iterable[int]] = None) -> None:
+    def __init__(
+        self,
+        matrix: np.ndarray,
+        *,
+        qid_shape: Optional[Iterable[int]] = None,
+        unitary_check_rtol: float = 1e-5,
+        unitary_check_atol: float = 1e-8,
+    ) -> None:
         """Initializes a matrix gate.
         Args:
             matrix: The matrix that defines the gate.
@@ -59,7 +66,7 @@ def __init__(self, matrix: np.ndarray, *, qid_shape: Optional[Iterable[int]] = N
                 f'qid_shape: {self._qid_shape}\n'
             )
 
-        if not linalg.is_unitary(matrix):
+        if not linalg.is_unitary(matrix, rtol=unitary_check_rtol, atol=unitary_check_atol):
             raise ValueError(f'Not a unitary matrix: {self._matrix}')
 
     def _json_dict_(self) -> Dict[str, Any]:

cirq-core/cirq/ops/matrix_gates_test.py

@@ -299,3 +299,26 @@ def test_protocols_and_repr():
     cirq.testing.assert_implements_consistent_protocols(
         cirq.MatrixGate(np.diag([1, 1j, -1]), qid_shape=(3,))
     )
+
+
+def test_matrixgate_unitary_tolerance():
+    ## non-unitary matrix
+    with pytest.raises(ValueError):
+        _ = cirq.MatrixGate(np.array([[1, 0], [0, -0.6]]), unitary_check_atol=0.5)
+
+    # very high atol -> check converges quickly
+    _ = cirq.MatrixGate(np.array([[1, 0], [0, 1]]), unitary_check_atol=1)
+
+    # very high rtol -> check converges quickly
+    _ = cirq.MatrixGate(np.array([[1, 0], [0, -0.6]]), unitary_check_rtol=1)
+
+    ## unitary matrix
+    _ = cirq.MatrixGate(np.array([[0.707, 0.707], [-0.707, 0.707]]), unitary_check_atol=0.5)
+
+    # very low atol -> the check never converges
+    with pytest.raises(ValueError):
+        _ = cirq.MatrixGate(np.array([[0.707, 0.707], [-0.707, 0.707]]), unitary_check_atol=1e-10)
+
+    # very low atol -> the check never converges
+    with pytest.raises(ValueError):
+        _ = cirq.MatrixGate(np.array([[0.707, 0.707], [-0.707, 0.707]]), unitary_check_rtol=1e-10)