# \`qml.prod\` vs direct operators product
**URL:** https://discuss.pennylane.ai/t/qml-prod-vs-direct-operators-product/3873
**Category:** PennyLane Help
**Created:** [January 8, 2024, 4:23pm UTC](https://discuss.pennylane.ai/t/qml-prod-vs-direct-operators-product/3873 "2024-01-08T16:23:14Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@Yian\_Chen](https://discuss.pennylane.ai/u/Yian_Chen)
#### Post date: [January 8, 2024, 4:23pm UTC](https://discuss.pennylane.ai/t/qml-prod-vs-direct-operators-product/3873/1 "2024-01-08T16:23:14Z")
When creating multi-product of observables, I found something acting out of my expectation. I think it should be clear to just demonstrate it with some codes below:
### Case 1
```python
before = qml.PauliX(wires=0)
after = before @ qml.PauliZ(wires=2)
print(f"Before = {before}")
print(f"After = {after}")
```
```bash
Before = PauliX(wires=[0])
After = PauliX(wires=[0]) @ PauliZ(wires=[2])
```
It works fine as my expectation, `before` is still `before`.
### Case 2
```python
before = qml.PauliX(wires=0) @ qml.PauliY(wires=1)
after = before @ qml.PauliZ(wires=2)
print(f"Before = {before}")
print(f"After = {after}")
```
```bash
Before = PauliX(wires=[0]) @ PauliY(wires=[1]) @ PauliZ(wires=[2])
After = PauliX(wires=[0]) @ PauliY(wires=[1]) @ PauliZ(wires=[2])
```
Now `before` is not `before` anymore, but seems to be contaminated.
### Case 3
If we write a for loop to see the behavior in more qubits:
```python
from functools import reduce
for num_wires in range(1, 5):
before = reduce(lambda x, y: x @ y, [qml.PauliX(wires=i) for i in range(num_wires)])
after = before @ qml.PauliZ(wires=num_wires)
print(f"`before` with {num_wires} wires:")
print(f"Before = {before}")
print(f"After = {after}")
print()
```
```bash
`before` with 1 wires:
Before = PauliX(wires=[0])
After = PauliX(wires=[0]) @ PauliZ(wires=[1])
`before` with 2 wires:
Before = PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliZ(wires=[2])
After = PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliZ(wires=[2])
`before` with 3 wires:
Before = PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2]) @ PauliZ(wires=[3])
After = PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2]) @ PauliZ(wires=[3])
`before` with 4 wires:
Before = PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2]) @ PauliX(wires=[3]) @ PauliZ(wires=[4])
After = PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2]) @ PauliX(wires=[3]) @ PauliZ(wires=[4])
```
We see that when `before` is a product of more than 1 observables, `before` will be contaminated from other behavior.
### Solution
Instead, if we change the syntax from `x @ y` to `qml.prod(x, y)`, it works correctly.
```python
for num_wires in range(1, 5):
before = reduce(lambda x, y: x @ y, [qml.PauliX(wires=i) for i in range(num_wires)])
after = qml.prod(before, qml.PauliZ(wires=num_wires))
print(f"`before` with {num_wires} wires:")
print(f"Before = {before}")
print(f"After = {after}")
print()
```
```bash
`before` with 1 wires:
Before = PauliX(wires=[0])
After = PauliX(wires=[0]) @ PauliZ(wires=[1])
`before` with 2 wires:
Before = PauliX(wires=[0]) @ PauliX(wires=[1])
After = (PauliX(wires=[0]) @ PauliX(wires=[1])) @ PauliZ(wires=[2])
`before` with 3 wires:
Before = PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2])
After = (PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2])) @ PauliZ(wires=[3])
`before` with 4 wires:
Before = PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2]) @ PauliX(wires=[3])
After = (PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2]) @ PauliX(wires=[3])) @ PauliZ(wires=[4])
```
### Conclusion
Iām not sure whether this is an intended design that we should use `qml.prod(x, y)` instead of `x @ y`, maybe I have miss somewhere in the document. If there is some detail discussion about this, it would be nice for me to take a look, thanks in advance.
### PennyLane version
```bash
Name: PennyLane
Version: 0.33.1
Summary: PennyLane is a Python quantum machine learning library by Xanadu Inc.
Home-page: https://github.com/PennyLaneAI/pennylane
Author:
Author-email:
License: Apache License 2.0
Location: /Users/yianchen/.pyenv/versions/3.9.12/lib/python3.9/site-packages
Requires: appdirs, autograd, autoray, cachetools, networkx, numpy, pennylane-lightning, requests, rustworkx, scipy, semantic-version, toml, typing-extensions
Required-by: PennyLane-Lightning
Platform info: macOS-12.6-x86_64-i386-64bit
Python version: 3.9.12
Numpy version: 1.23.5
Scipy version: 1.11.4
Installed devices:
- default.gaussian (PennyLane-0.33.1)
- default.mixed (PennyLane-0.33.1)
- default.qubit (PennyLane-0.33.1)
- default.qubit.autograd (PennyLane-0.33.1)
- default.qubit.jax (PennyLane-0.33.1)
- default.qubit.legacy (PennyLane-0.33.1)
- default.qubit.tf (PennyLane-0.33.1)
- default.qubit.torch (PennyLane-0.33.1)
- default.qutrit (PennyLane-0.33.1)
- null.qubit (PennyLane-0.33.1)
- lightning.qubit (PennyLane-Lightning-0.33.1)
```
---
### Author:  [@christina](https://discuss.pennylane.ai/u/christina)
#### Post date: [January 9, 2024, 5:10pm UTC](https://discuss.pennylane.ai/t/qml-prod-vs-direct-operators-product/3873/2 "2024-01-09T17:10:37Z")
Thanks for the post @Yian_Chen .
You can change the behaviour of the operator dunder methods (`@`) by running `qml.operation.enable_new_opmath()`. This will give you sums, products, and scalar products instead of `Tensor` and `Hamiltonian`.
You can see the documentation for this function: [qml.operation.enable\_new\_opmath ā PennyLane 0.34.0 documentation](https://docs.pennylane.ai/en/stable/code/api/pennylane.operation.enable_new_opmath.html)
We hope to change the default behavior in the near future.
---
### Author:  [@Yian\_Chen](https://discuss.pennylane.ai/u/Yian_Chen)
#### Post date: [January 10, 2024, 6:02am UTC](https://discuss.pennylane.ai/t/qml-prod-vs-direct-operators-product/3873/3 "2024-01-10T06:02:50Z")
Hi @Christina , thank you, this works for me š