Fix: Avoid cotengra bug for empty contraction paths and add tests

- Handle len(raw_tensors) == 0 by returning a scalar identity tensor.
- Handle len(raw_tensors) == 1 by using be.einsum directly.
- Guard against IndexError when accessing nodes[0].backend.
- Ensure exponent is initialized for these edge cases.
- Add edge case tests in tests/test_hyperedge.py for 0 and 1 tensor cases.

Co-authored-by: refraction-ray <35157286+refraction-ray@users.noreply.github.com>

Author: google-labs-jules[bot]

tensorcircuit/cons.py

@@ -587,9 +587,16 @@ def _algebraic_base_contraction(
 
     raw_tensors, input_sets, output_set, size_dict = _extract_topology(nodes)
     # Use the backend of the first node
-    be = nodes[0].backend
+    if len(nodes) > 0:
+        be = nodes[0].backend
+    else:
+        be = get_backend(get_default_backend())
 
-    if len(raw_tensors) == 1:
+    if len(raw_tensors) == 0:
+        # Avoid cotengra bug for empty contraction paths
+        final_raw_tensor = be.ones([])
+        exponent = 0.0
+    elif len(raw_tensors) == 1:
         # Avoid cotengra bug for empty contraction paths
         final_raw_tensor = be.einsum(input_sets[0] + "->" + output_set, *raw_tensors)
         exponent = 0.0

tests/test_hyperedge.py

@@ -545,3 +545,24 @@ def test_qir_fallback(contractor_setup, backend):
     qir = c.to_qir()
     c2 = tc.Circuit.from_qir(qir, circuit_params={"nqubits": n})
     np.testing.assert_allclose(c.state(), c2.state(), atol=1e-5)
+
+@pytest.mark.parametrize("contractor_setup", [("cotengra", {"use_primitives": True})], indirect=True)
+def test_algebraic_contraction_edge_cases(contractor_setup, backend_setup):
+    from tensorcircuit.cons import _algebraic_base_contraction
+    import opt_einsum
+
+    # 0 nodes case
+    res0 = _algebraic_base_contraction([], opt_einsum.paths.greedy)
+    np.testing.assert_allclose(tc.backend.numpy(res0.tensor), 1.0)
+
+    # 1 node case
+    a = tn.Node(tc.backend.convert_to_tensor(np.array([1.0, 2.0])))
+    res1 = _algebraic_base_contraction([a], opt_einsum.paths.greedy)
+    np.testing.assert_allclose(tc.backend.numpy(res1.tensor), np.array([1.0, 2.0]))
+
+    # 1 node with self-loop (trace)
+    # _extract_topology handles traces by mapping them to symbols
+    b = tn.Node(tc.backend.convert_to_tensor(np.eye(2)))
+    b[0] ^ b[1]
+    res1_trace = _algebraic_base_contraction([b], opt_einsum.paths.greedy)
+    np.testing.assert_allclose(tc.backend.numpy(res1_trace.tensor), 2.0)