`torch.complex` fails Edge export and CPU execution

🐛 Describe the bug

A model using torch.complex(real, imag) can be captured with torch.export.export(), but cannot complete the default ExecuTorch export-to-runtime workflow.

There are two failures:

1. Default to_edge() rejects aten.complex.default because it is not in PyTorch's Core ATen opset.
2. Explicitly allowing that operator enables export, but CPU execution fails because aten::complex.out has no registered kernel.

Minimal reproduction

import traceback

import torch
from torch.export import export
from executorch.exir import EdgeCompileConfig, to_edge
from executorch.runtime import Runtime

class Complex(torch.nn.Module):
    def forward(self, real, imag):
        return torch.complex(real, imag)

real = torch.tensor([1.0, 2.0], dtype=torch.float32)
imag = torch.tensor([3.0, 4.0], dtype=torch.float32)
exported = export(Complex(), (real, imag))

# First failure: default Edge verification.
try:
    to_edge(exported)
except Exception:
    traceback.print_exc()

# Second failure: missing CPU kernel after explicitly allowing the operator.
program = to_edge(
    exported,
    compile_config=EdgeCompileConfig(
        _core_aten_ops_exception_list=[torch.ops.aten.complex.default]
    ),
).to_executorch()

method = Runtime.get().load_program(program.buffer).load_method("forward")
outputs = method.execute([real, imag])
print(outputs)

Actual behavior

First failure:

torch._export.verifier.SpecViolationError:
Operator torch._ops.aten.complex.default is not in Core ATen opset (https://pytorch.org/docs/stable/torch.compiler_ir.html#core-aten-ir)."

Second failure:

RuntimeError: Failed to load method forward, error: 0x14: kernel 'aten::complex.out' not found.; Missing operator: [0] aten::complex.out; There are 1 instructions don't have corresponding operator registered. See logs for detail

Expected behavior

The model should produce a complex64 tensor equivalent to

torch.tensor([1 + 3j, 2 + 4j], dtype=torch.complex64)

The same workflow should support matching float16 and float64 inputs, producing complex32 and complex128 outputs respectively.

Versions

PyTorch version: 2.14.0+cu130
Is debug build: False
CUDA used to build PyTorch: 13.0
ROCm SDK used to build PyTorch: N/A
HIP used to build PyTorch: N/A

OS: Ubuntu 24.04.5 LTS (aarch64)
GCC version: (Ubuntu 13.3.0-6ubuntu2~24.04.1) 13.3.0
Clang version: Could not collect
CMake version: version 3.31.10
Libc version: glibc-2.39

Python version: 3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0] (64-bit runtime)
Python platform: Linux-7.0.0-1019-nvidia-aarch64-with-glibc2.39
Is CUDA available: True
CUDA runtime version: 13.0.88
CUDA_MODULE_LOADING set to:
GPU models and configuration: GPU 0: NVIDIA GB10
Nvidia driver version: 580.178.04
cuDNN version: Probably one of the following:
/usr/lib/aarch64-linux-gnu/libcudnn.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_adv.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_cnn.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_engines_precompiled.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_engines_runtime_compiled.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_engines_tensor_ir.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_ext.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_graph.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_heuristic.so.9.27.0
/usr/lib/aarch64-linux-gnu/libcudnn_ops.so.9.27.0
Is XPU available: False
HIP runtime version: N/A
MIOpen runtime version: N/A
Is XNNPACK available: False
Caching allocator config: N/A

CPU:
Architecture: aarch64
CPU op-mode(s): 64-bit
Byte Order: Little Endian
CPU(s): 20
On-line CPU(s) list: 0-19
Vendor ID: ARM
Model name: Cortex-X925
Model: 1
Thread(s) per core: 1
Core(s) per socket: 10
Socket(s): 1
Stepping: r0p1
Frequency boost: disabled
CPU(s) scaling MHz: 100%
CPU max MHz: 3900.0000
CPU min MHz: 1378.0000
BogoMIPS: 2000.00
Flags: fp asimd evtstrm aes pmull sha1 sha2 crc32 atomics fphp asimdhp cpuid asimdrdm jscvt fcma lrcpc dcpop sha3 sm3 sm4 asimddp sha512 sve asimdfhm dit uscat ilrcpc flagm sb paca pacg dcpodp sve2 sveaes svepmull svebitperm svesha3 svesm4 flagm2 frint svei8mm svebf16 i8mm bf16 dgh bti ecv afp wfxt
Model name: Cortex-A725
Model: 1
Thread(s) per core: 1
Core(s) per socket: 10
Socket(s): 1
Stepping: r0p1
CPU(s) scaling MHz: 100%
CPU max MHz: 2808.0000
CPU min MHz: 338.0000
BogoMIPS: 2000.00
Flags: fp asimd evtstrm aes pmull sha1 sha2 crc32 atomics fphp asimdhp cpuid asimdrdm jscvt fcma lrcpc dcpop sha3 sm3 sm4 asimddp sha512 sve asimdfhm dit uscat ilrcpc flagm sb paca pacg dcpodp sve2 sveaes svepmull svebitperm svesha3 svesm4 flagm2 frint svei8mm svebf16 i8mm bf16 dgh bti ecv afp wfxt
L1d cache: 1.3 MiB (20 instances)
L1i cache: 1.3 MiB (20 instances)
L2 cache: 25 MiB (20 instances)
L3 cache: 24 MiB (2 instances)
NUMA node(s): 1
NUMA node0 CPU(s): 0-19
Vulnerability Gather data sampling: Not affected
Vulnerability Ghostwrite: Not affected
Vulnerability Indirect target selection: Not affected
Vulnerability Itlb multihit: Not affected
Vulnerability L1tf: Not affected
Vulnerability Mds: Not affected
Vulnerability Meltdown: Not affected
Vulnerability Mmio stale data: Not affected
Vulnerability Old microcode: Not affected
Vulnerability Reg file data sampling: Not affected
Vulnerability Retbleed: Not affected
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1: Mitigation; __user pointer sanitization
Vulnerability Spectre v2: Mitigation; CSV2, BHB
Vulnerability Srbds: Not affected
Vulnerability Tsa: Not affected
Vulnerability Tsx async abort: Not affected
Vulnerability Vmscape: Not affected

Versions of relevant libraries:
[pip3] executorch==1.6.0+7586c16
[pip3] numpy==2.5.4
[pip3] nvidia-cublas==13.1.1.3
[pip3] nvidia-cuda-cupti==13.0.85
[pip3] nvidia-cuda-nvrtc==13.0.88
[pip3] nvidia-cuda-runtime==13.0.96
[pip3] nvidia-cudnn-cu13==9.24.0.43
[pip3] nvidia-cufft==12.0.0.61
[pip3] nvidia-curand==10.4.0.35
[pip3] nvidia-cusolver==12.0.4.66
[pip3] nvidia-cusparse==12.6.3.3
[pip3] nvidia-cusparselt-cu13==0.8.1
[pip3] nvidia-nccl-cu13==2.30.7
[pip3] nvidia-nvjitlink==13.4.92
[pip3] nvidia-nvtx==13.0.85
[pip3] optimum-executorch==0.2.0.dev0
[pip3] pytorch_tokenizers==1.4.0
[pip3] torch==2.14.0+cu130
[pip3] torchao==0.19.0.dev20260907+cpu
[pip3] triton==3.8.0+gitdf3f91dd
[conda] Could not collect

cc @larryliu0820 @manuelcandales @JakeStevens