[new opmath 1] Toggle __use_new_opmath

[Qottmann]

PR to toggle the __use_new_opmath and make it default.
This will require several changes in the codebase (and further updates to demos, dataset and plugins).
Bigger changes should be offloaded in separate PRs. Small updates can be gathered here.

Branching: #5269 > #5216 > #5322 > #5335

• Make sure lightning works

import os, sys
os.environ["OMP_NUM_THREADS"]="8"
import pennylane as qml
from pennylane import numpy as np
from timeit import default_timer as timer

if __name__ == "__main__":
    rng = np.random.default_rng(seed=1337)  # make the results reproducable
    mol = qml.data.load("qchem", molname="H2O", bondlength=0.958, basis="STO-3G")[0]

    hf_state = mol.hf_state
    ham = mol.hamiltonian
    wires = ham.wires
    dev = qml.device("lightning.qubit", wires=wires, batch_obs=True)

    n_electrons = mol.molecule.n_electrons
    singles, doubles = qml.qchem.excitations(n_electrons, len(wires))
    hf_state.requires_grad = False
    hf_ops = []

    for idx,i in enumerate(hf_state):
        if i==1:
            hf_ops.append((qml.PauliX, idx))

    @qml.qnode(dev, diff_method="adjoint")
    def cost(weights):
        for (x,i) in hf_ops: # HF state
            x(i)
        for idx,s in enumerate(singles):
            qml.SingleExcitation(weights[idx], wires=s)
        for idx,d in enumerate(doubles):
            qml.DoubleExcitation(weights[idx+len(singles)], wires=d)
        return qml.expval(ham)

    params = qml.numpy.array(rng.normal(0, np.pi, len(singles) + len(doubles)))
    opt = qml.GradientDescentOptimizer(stepsize=0.5)

    # store the values of the circuit parameter
    angle = [params]
    max_iterations = 50
    procs = int(os.getenv("PL_FWD_BATCH", "0"))
    pre_s = f"qubits={len(wires)},num_terms={len(ham.terms()[0])},procs={procs},"

    energies = []

    for n in range(max_iterations):
        start_grad = timer()
        params, prev_energy = opt.step_and_cost(cost, params)
        energies.append(prev_energy)
        end_grad = timer()
        angle.append(params)
        print(f"{pre_s},Step={n},Time_grad={end_grad-start_grad}")

    start_fwd = timer()
    energy = cost(params)
    energies.append(energy)
    end_fwd = timer()
    print(f"Energies={energies},Time_fwd={end_fwd - start_fwd}")

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
• A link back to this PR.
• Your name (or GitHub username) in the contributors section.

[albi3ro]

🎉