[BUG] Recursion error when accessing operator built using qml.prod

[asymptoticgains]

Expected behavior

Should be able to build time evolution operator that is a product of many Pauli rotations

Actual behavior

RecursionError: maximum recursion depth exceeded while calling a Python object

Additional information

It works fine if lazy=False is set in qml.prod. Seems like if there are too many nested operators in the result from taking qml.prod too many times, it will cause a recursion error. The limit seems to be about 800 terms; for example, setting range() to 370 in the for loop in attached source code runs fine.

Source code

import numpy as np 
import pennylane as qml
import random

time_ev = qml.PauliRot(random.uniform(0, 2 * np.pi), 'X', wires=1)
for i in range(500):
    time_ev = qml.prod(time_ev, qml.PauliRot(random.uniform(0, 2 * np.pi), 'Z', wires=1))
    time_ev = qml.prod(time_ev, qml.PauliRot(random.uniform(0, 2 * np.pi), 'Y', wires=1))

print(time_ev)

Tracebacks

---------------------------------------------------------------------------
RecursionError                            Traceback (most recent call last)
Cell In[10], line 10
      7     time_ev = qml.prod(time_ev, qml.PauliRot(random.uniform(0, 2 * np.pi), 'Z', wires=1))
      8     time_ev = qml.prod(time_ev, qml.PauliRot(random.uniform(0, 2 * np.pi), 'Y', wires=1))
---> 10 print(time_ev)

File ~/.conda/envs/xanadu/lib/python3.9/site-packages/pennylane/ops/op_math/composite.py:80, in CompositeOp.__repr__(self)
     78 def __repr__(self):
     79     return f" {self._op_symbol} ".join(
---> 80         [f"({op})" if op.arithmetic_depth > 0 else f"{op}" for op in self]
     81     )

File ~/.conda/envs/xanadu/lib/python3.9/site-packages/pennylane/ops/op_math/composite.py:80, in <listcomp>(.0)
     78 def __repr__(self):
     79     return f" {self._op_symbol} ".join(
---> 80         [f"({op})" if op.arithmetic_depth > 0 else f"{op}" for op in self]
     81     )

File ~/.conda/envs/xanadu/lib/python3.9/site-packages/pennylane/ops/op_math/prod.py:384, in Prod.arithmetic_depth(self)
    382 @property
    383 def arithmetic_depth(self) -> int:
--> 384     return 1 + max(factor.arithmetic_depth for factor in self)

File ~/.conda/envs/xanadu/lib/python3.9/site-packages/pennylane/ops/op_math/prod.py:384, in <genexpr>(.0)
...
     94 def __iter__(self):
     95     """Return the iterator over the underlying operands."""
---> 96     return iter(self.operands)

System information

Name: PennyLane
Version: 0.36.0
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: /home/serene.shum/.conda/envs/xanadu/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-qiskit, PennyLane_Lightning, vibrant

Platform info:           Linux-6.5.0-41-generic-x86_64-with-glibc2.35
Python version:          3.9.19
Numpy version:           1.26.4
Scipy version:           1.13.0
Installed devices:
- default.clifford (PennyLane-0.36.0)
- default.gaussian (PennyLane-0.36.0)
- default.mixed (PennyLane-0.36.0)
- default.qubit (PennyLane-0.36.0)
- default.qubit.autograd (PennyLane-0.36.0)
- default.qubit.jax (PennyLane-0.36.0)
- default.qubit.legacy (PennyLane-0.36.0)
- default.qubit.tf (PennyLane-0.36.0)
- default.qubit.torch (PennyLane-0.36.0)
- default.qutrit (PennyLane-0.36.0)
- default.qutrit.mixed (PennyLane-0.36.0)
- null.qubit (PennyLane-0.36.0)
- lightning.qubit (PennyLane-Lightning-0.36.0)
- qiskit.aer (PennyLane-qiskit-0.36.0)
- qiskit.basicaer (PennyLane-qiskit-0.36.0)
- qiskit.basicsim (PennyLane-qiskit-0.36.0)
- qiskit.ibmq (PennyLane-qiskit-0.36.0)
- qiskit.ibmq.circuit_runner (PennyLane-qiskit-0.36.0)
- qiskit.ibmq.sampler (PennyLane-qiskit-0.36.0)
- qiskit.remote (PennyLane-qiskit-0.36.0)

Existing GitHub issues

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