[Draft] Place coding examples with legacy-like structure

[Doomsk]

Add example given by João to compare with current Qadence 1 code:

# Qadence 1
import torch
import matplotlib.pyplot as plt

from qadence import RX, Z, FeatureParameter
from qadence import QuantumCircuit, QuantumModel, BackendName


n_qubits = 1
x = FeatureParameter("x")
block = RX(0, x)
circuit = QuantumCircuit(n_qubits, block)
observable = Z(0)
model = QuantumModel(circuit, observable, backend = BackendName.PYQTORCH)


x = torch.arange(0, 2 * torch.pi, 0.1, requires_grad = True)
values = {"x": x}

fx = model.expectation(values).squeeze()
dfdx = torch.autograd.grad(
        outputs=fx,
        inputs=x,
        grad_outputs = torch.ones_like(x),
    )[0]

plt.plot(x.detach(), fx.detach(), label = "f(x)")
plt.plot(x.detach(), dfdx.detach(), label = "df/dx")
plt.legend()

and Qadence 2:

# Qadence 2
import torch
import matplotlib.pyplot as plt

from qadence2_expressions import RX, Z, parameter
from qadence2.extensions.legacy import QuantumModel

x = parameter("x")
expr = RX(x)(0)
model = QuantumModel(expr, backend="pyqtorch")

x = torch.arange(0, 2 * torch.pi, 0.1, requires_grad=True)
values = {"x": x}

fx = model.expectation(values=values, observable=Z(0)).squeeze()
dfdx = torch.autograd.grad(
    outputs=fx,
    inputs=x,
    grad_outputs=torch.ones_like(x),
)[0]

plt.plot(x.detach(), fx.detach(), label="f(x)")
plt.plot(x.detach(), dfdx.detach(), label="df/dx")
plt.legend()

[jpmoutinho]

One question, if you consider this to be a "legacy-like" structure, is there some specific new structure that should be used instead? If yes, it would be good to have the examples in that format as well.

[RolandMacDoland]

Just an intermediary review. Minor comments there otherwise LGTM.

[RolandMacDoland]

Same.

[RolandMacDoland]

Maybe more comment about what this constant is and units.

[Doomsk]

@jpmoutinho

[RolandMacDoland]

I guess it's better to remove pinning the dependencies ?