[BUG]qnode execution on simulators slows down with increasing commuting Hamiltonian terms

Expected behavior

With compute_grouping I would expect the following two qnodes, circuit() and circuit2(), to have similar execution time.

import pennylane as qml
from pennylane import numpy as np
import time

n_qubits = 15

H_quad = 0 * qml.PauliZ(0)
for i in range(n_qubits):
    for j in range(i + 1, n_qubits):
        H_quad += qml.PauliZ(i) @ qml.PauliZ(j)
H_quad.compute_grouping()

H_lin = 0 * qml.PauliZ(0)
for i in range(n_qubits):
    H_lin += qml.PauliZ(i)
H_lin.compute_grouping()

dev = qml.device("lightning.qubit", wires=n_qubits, shots=1000)
@qml.qnode(dev)
def circuit():
    for w in range(n_qubits):
        qml.Hadamard(wires=w)
    return qml.expval(H_quad)

@qml.qnode(dev)
def circuit2():
    for w in range(n_qubits):
        qml.Hadamard(wires=w)
    return qml.expval(H_lin)


start = time.time()
circuit()
end = time.time()
print(f"qnode with quadratic terms: {end - start}s")

start = time.time()
circuit2()
end = time.time()
print(f"qnode with linear terms: {end - start}s")

Actual behavior

The qnode with quadratic terms executes significantly slower. Printed result from the code above:

qnode with quadratic terms: 0.8156991004943848s
qnode with linear terms: 0.004673004150390625s

Additional information

The observation holds for both default.qubit and lightning.qubit.

Source code

No response

Tracebacks

No response

System information

Name: PennyLane
Version: 0.22.0
Summary: PennyLane is a Python quantum machine learning library by Xanadu Inc.
Home-page: https://github.com/XanaduAI/pennylane
Author: 
Author-email: 
License: Apache License 2.0
Location: /home/ec2-user/anaconda3/envs/Braket/lib/python3.7/site-packages
Requires: semantic-version, autograd, appdirs, numpy, autoray, pennylane-lightning, scipy, toml, cachetools, networkx, retworkx
Required-by: PennyLane-Qchem, PennyLane-Lightning, amazon-braket-pennylane-plugin
Platform info:           Linux-4.14.252-131.483.amzn1.x86_64-x86_64-with-glibc2.17
Python version:          3.7.13
Numpy version:           1.19.2
Scipy version:           1.5.2
Installed devices:
- default.gaussian (PennyLane-0.22.0)
- default.mixed (PennyLane-0.22.0)
- default.qubit (PennyLane-0.22.0)
- default.qubit.autograd (PennyLane-0.22.0)
- default.qubit.jax (PennyLane-0.22.0)
- default.qubit.tf (PennyLane-0.22.0)
- default.qubit.torch (PennyLane-0.22.0)
- lightning.qubit (PennyLane-Lightning-0.23.0)
- braket.aws.qubit (amazon-braket-pennylane-plugin-1.6.5)
- braket.local.qubit (amazon-braket-pennylane-plugin-1.6.5)

Existing GitHub issues

• I have searched existing GitHub issues to make sure the issue does not already exist.

[duanyh12]

@Jaybsoni Hi Jay. Thanks for investigating. For 1, I am even wondering if resolving this issue could improve the overall QAOA ansatz layer execution efficiency (not limited to the measurement). Keep me posted!

[Jaybsoni]

Hi @duanyh12,

Great suggestion! Yes, Identity operators will commute with every other observable so we shouldn’t have to worry about them in these qwc checks. I think we can actually further build on this idea to get an even better boost in performance. Here is a new feature request I have created where we can discuss how to further improve the performance