Support all operations with `param_shift_hessian()`

Feature details

It should be possible to support operations with arbitrary grad_recipes in param_shift_hessian() by computing the applicable grad recipe for each entry in the hessian from the grad_recipess of the operations instead of using fixed diag_recipe and off_diag_recipes.

A first and easier improvement would be to at least replace the hard coded list of “supported operations” by code that inspects the grad_recipes of the occuring operations so that newly added operations that are also differentiable according to the standard rule are supported automatically.

Implementation

No response

How important would you say this feature is?

2: Somewhat important. Needed this quarter.

Additional information

No response

[soranjh]

For the first bug, the problem seems to stem from the behaviour of tape.trainable_params together with the Hamiltonian:

dev = qml.device('default.qubit', wires=2)
qubit_operator = of.QubitOperator('X0 Y1', 1.0)
hamiltonian = qml.import_operator(qubit_operator)
hamiltonian.coeffs.requires_grad = False

@qml.qnode(dev, diff_method='parameter-shift')
def circuit(param):
    qml.RY(param, wires=[0])
    return qml.expval(hamiltonian)

>>> param = np.array(0.2, requires_grad=True)
>>> circuit.construct((params,), {})
>>> print(circuit.qtape.trainable_params)
[0, 1]

As we can see, the Hamiltonian coefficient is set to be trainable.

Setting requires_grad = False for the Hamiltonian coefficients seems to solve the issue:

dev = qml.device('default.qubit', wires=2)
qubit_operator = of.QubitOperator('X0 Y1', 1.0)
hamiltonian = qml.import_operator(qubit_operator)

c = np.array(hamiltonian.coeffs, requires_grad = False)
o = hamiltonian.ops
hamiltonian = qml.Hamiltonian(c, o)

@qml.qnode(dev, diff_method='parameter-shift')
def circuit(param):
    qml.RY(param, wires=[0])
    return qml.expval(hamiltonian)

params = np.array(0.2, requires_grad=True)
circuit.construct((params,), {})
print(circuit.qtape.trainable_params) # output: [0]

Not sure why hamiltonian.coeffs.requires_grad = True does not do the same thing.

[cvjjm]

I don’t know yet what will be useful, so I would say it generalizes 😃

Maybe the user can pass in a “mask” of the same shape as the hessian with boolean entries and then get a hessian with only those entries back?