# Error using adjoint differentiation for metric tensor with complex statevector outputs
**URL:** https://discuss.pennylane.ai/t/error-using-adjoint-differentiation-for-metric-tensor-with-complex-statevector-outputs/8758
**Category:** PennyLane Help
**Created:** [July 15, 2025, 1:39pm UTC](https://discuss.pennylane.ai/t/error-using-adjoint-differentiation-for-metric-tensor-with-complex-statevector-outputs/8758 "2025-07-15T13:39:46Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@a.rozgonyi96](https://discuss.pennylane.ai/u/a.rozgonyi96)
#### Post date: [July 15, 2025, 1:39pm UTC](https://discuss.pennylane.ai/t/error-using-adjoint-differentiation-for-metric-tensor-with-complex-statevector-outputs/8758/1 "2025-07-15T13:39:46Z")
Hi!
I came across an issue when I applied `diff_method="adjoint"` using JAX backend under the hood of built-in `metric_tensor`. Seems like JAX only allows real‐valued outputs for reverse‐mode differentation. Since the QNode returns the full quantum state (a complex vector), we must tell JAX to treat the function as holomorphic.
I could workaround, as I use `qml.expval()`, however in that case later when I optimize the circuit I run into a `ProbabilityMP` error. I would appreciate any advice on how to use adjoint differentiation and JAX and full state.
Here is my code:
```auto
dev = qml.device('default.qubit')
# Parameter values
theta = jnp.array([jnp.pi / 2, jnp.pi / 2]) # One theta per node
@qml.qnode(dev, interface="jax", diff_method="adjoint")
def circuit(theta):
# Hamiltonian
obs = [qml.Z(0), qml.X(1)]
H_Z = qml.Hamiltonian(theta, obs)
# Dynamics
n = 3 # number of Trotter steps
for _ in range(n):
qml.ApproxTimeEvolution(H_Z, 1/n, 1)
# Return
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))
QFIM = 4*qml.gradients.metric_tensor(circuit)(theta)
print(QFIM)
```
This is the error message I get:
```auto
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/tmp/ipython-input-99-1342454709.py in ()
----> 1 QFIM = 4*qml.gradients.metric_tensor(circuit)(theta)
2 print(QFIM)
10 frames
/usr/local/lib/python3.11/dist-packages/jax/_src/api.py in _check_output_dtype_revderiv(name, holomorphic, x)
759 f"but got {aval.dtype.name}.")
760 elif dtypes.issubdtype(aval.dtype, np.complexfloating):
--> 761 raise TypeError(f"{name} requires real-valued outputs (output dtype that is "
762 f"a sub-dtype of np.floating), but got {aval.dtype.name}. "
763 "For holomorphic differentiation, pass holomorphic=True. "
TypeError: jacrev requires real-valued outputs (output dtype that is a sub-dtype of np.floating), but got complex128. For holomorphic differentiation, pass holomorphic=True. For differentiation of non-holomorphic functions involving complex outputs, use jax.vjp directly.
```
The Pennylane version I used:
```auto
Name: PennyLane
Version: 0.41.1
Summary: PennyLane is a cross-platform Python library for quantum computing, quantum machine learning, and quantum chemistry. Train a quantum computer the same way as a neural network.
Home-page: https://github.com/PennyLaneAI/pennylane
Author:
Author-email:
License: Apache License 2.0
Location: /usr/local/lib/python3.11/dist-packages
Requires: appdirs, autograd, autoray, cachetools, diastatic-malt, networkx, numpy, packaging, pennylane-lightning, requests, rustworkx, scipy, tomlkit, typing-extensions
Required-by: PennyLane_Lightning
Platform info: Linux-6.1.123+-x86_64-with-glibc2.35
Python version: 3.11.13
Numpy version: 2.0.2
Scipy version: 1.15.3
Installed devices:
- lightning.qubit (PennyLane_Lightning-0.41.1)
- default.clifford (PennyLane-0.41.1)
- default.gaussian (PennyLane-0.41.1)
- default.mixed (PennyLane-0.41.1)
- default.qubit (PennyLane-0.41.1)
- default.qutrit (PennyLane-0.41.1)
- default.qutrit.mixed (PennyLane-0.41.1)
- default.tensor (PennyLane-0.41.1)
- null.qubit (PennyLane-0.41.1)
- reference.qubit (PennyLane-0.41.1)
```
---
### Author:  [@a.rozgonyi96](https://discuss.pennylane.ai/u/a.rozgonyi96)
#### Post date: [July 16, 2025, 11:40am UTC](https://discuss.pennylane.ai/t/error-using-adjoint-differentiation-for-metric-tensor-with-complex-statevector-outputs/8758/2 "2025-07-16T11:40:47Z")
I’m sorry, seems like updating PennyLane to 0.42 solved the issue.
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