pennylane: [BUG] With many observables `generate_shifted_tapes()` is called "unreasonably often" resulting in massive performance loss

Expected behavior

When taking the parameter shift hessian of a QNode returning the expectation value of several compatible observables, I expect the construction of shifted tapes to only take place once per gate, then the derivatives of all observables can be computed from this single set of shifted gates.

Actual behavior

In reality parameter_shift.py:152:expval_param_shift is called for each observable separately and generate_shifted_tapes() is therefore called number of parametrized gates times number of observables many times.

This results in a massive performance hit. In the 10 qubit example below, PennyLane spends over 60% of the time copying tapes, compared to just ~4% with the simulation of circuits, even on the slow default.qubit simulator.

Additional information

To get a nice graphical overview of what is happening run the example below with cProfile, e.g… like this: python -m cProfile -o timing test.py && gprof2dot -f pstats timing -o graph.dot && dot -Tsvg graph.dot -o graph.svg

Source code

# test.py 
# run with:
# python -m cProfile -o timing test.py && gprof2dot -f pstats timing -o graph.dot && dot -Tsvg graph.dot -o graph.svg
import pennylane as qml
from pennylane import numpy as np

num_wires = 10
wires = range(num_wires)
dev = qml.device('default.qubit', num_wires)

np.random.seed(42)
init_params = np.random.randn(num_wires//2)

@qml.qnode(dev, diff_method='parameter-shift')
def qnode(params):
    for par_idx, wire in enumerate(wires[::2]):
        qml.Hadamard(wire)
        qml.CRY(params[par_idx], wires=[wire, wire+1])
    return [qml.expval(qml.PauliZ(wire1) @ qml.PauliZ(wire2)) for wire1 in wires for wire2 in wires if wire1 != wire2]

print(len([0 for wire1 in wires for wire2 in wires if wire1 != wire2]))

for _ in range(4):
    print(qml.jacobian(qnode)(init_params))

Tracebacks

No response

System information

Python 3.8.8 | packaged by conda-forge | (default, Feb 20 2021, 16:22:27)
[GCC 9.3.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import pennylane as qml; qml.about()
WARNING: pip is being invoked by an old script wrapper. This will fail in a future version of pip.
Please see https://github.com/pypa/pip/issues/5599 for advice on fixing the underlying issue.
To avoid this problem you can invoke Python with '-m pip' instead of running pip directly.
Name: PennyLane
Version: 0.21.0.dev0
Summary: PennyLane is a Python quantum machine learning library by Xanadu Inc.
Home-page: https://github.com/XanaduAI/pennylane
Author: None
Author-email: None
License: Apache License 2.0
Location: /home/cvjjm/src/covqcstack/qcware/pennylane
Requires: numpy, scipy, networkx, retworkx, autograd, toml, appdirs, semantic-version, autoray, cachetools, pennylane-lightning
Required-by: pytket-pennylane, PennyLane-Qchem, PennyLane-Lightning, covvqetools
Platform info:           Linux-5.10.102.1-microsoft-standard-WSL2-x86_64-with-glibc2.10
Python version:          3.8.8
Numpy version:           1.20.1
Scipy version:           1.6.1
Installed devices:
- default.gaussian (PennyLane-0.21.0.dev0)
- default.mixed (PennyLane-0.21.0.dev0)
- default.qubit (PennyLane-0.21.0.dev0)
- default.qubit.autograd (PennyLane-0.21.0.dev0)
- default.qubit.jax (PennyLane-0.21.0.dev0)
- default.qubit.tf (PennyLane-0.21.0.dev0)
- default.qubit.torch (PennyLane-0.21.0.dev0)
- pytket.pytketdevice (pytket-pennylane-0.1.0)
- lightning.qubit (PennyLane-Lightning-0.20.2)
- cov.qubit (covvqetools-0.1.1)

Existing GitHub issues

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