Optimizing is mutually orthogonal function.

toqito/state_props/is_mutually_orthogonal.py

@@ -61,9 +61,15 @@ def is_mutually_orthogonal(vec_list: list[np.ndarray | list[float | Any]]) -> bo
     if len(vec_list) <= 1:
         raise ValueError("There must be at least two vectors provided as input.")
 
-    for i, vec_1 in enumerate(vec_list):
-        for j, vec_2 in enumerate(vec_list):
-            if i != j:
-                if not np.isclose(np.inner(vec_1.conj().T, vec_2.conj().T), 0):
-                    return False
-    return True
+    # Convert list of vectors to a 2D array (each vector is a column)
+    mat = np.column_stack(vec_list)
+
+    # Compute the matrix of inner products
+    inner_product_matrix = np.dot(mat.T.conj(), mat)
+
+    # The diagonal elements will be non-zero (norm of each vector)
+    # Set the diagonal elements to zero for the comparison
+    np.fill_diagonal(inner_product_matrix, 0)
+
+    # Check if all off-diagonal elements are close to zero
+    return np.allclose(inner_product_matrix, 0)

toqito/state_props/tests/test_is_mutually_orthogonal.py

@@ -11,6 +11,18 @@
     ([bell(0), bell(1), bell(2), bell(3)], True),
     # Return False for non-orthogonal vectors.
     ([np.array([1, 0]), np.array([1, 1])], False),
+    # Orthogonal vectors in R^2
+    ([np.array([1, 0]), np.array([0, 1])], True),
+    # Orthogonal vectors in R^2
+    ([np.array([1, 0, 0]), np.array([0, 1, 0]), np.array([0, 0, 1])], True),
+    # Orthogonal complex-valued vectors
+    ([np.array([[1], [1j]]), np.array([[1j], [1]])], True),
+    # Vectors with zero elements.
+    ([np.array([[0], [0]]), np.array([[1], [0]])], True),
+    # Colinear vectors.
+    ([np.array([[1], [2]]), np.array([2, 4])], False),
+    # Vectors that are theoretically orthogonal but due to numerical precision issues might not be exactly orthogonal.
+    ([np.array([[1], [np.sqrt(2)]]), np.array([[-np.sqrt(2)], [1]])], True),
 ])
 def test_is_mutually_orthogonal(states, expected_result):
     np.testing.assert_equal(is_mutually_orthogonal(states), expected_result)
@@ -19,6 +31,12 @@ def test_is_mutually_orthogonal(states, expected_result):
 @pytest.mark.parametrize("states", [
     # Tests for invalid input len.
     ([np.array([1, 0])]),
+    # Single vector should raise error.
+    ([np.array([[1], [2], [3]])]),
+    # Vectors of differing lengths.
+    ([np.array([[1], [0]]), np.array([[1], [0], [1]])]),
+    # Empty vector.
+    ([]),
 ])
 def test_is_mutually_orthogonal_basis_invalid_input(states):
     with np.testing.assert_raises(ValueError):