Supporting time-dependent Hamiltonian for time-evolution

[yulunwang]

Feature details

Hi all,

I am trying to use Pennylane to solve time evolution problems, where the Hamiltonian is time-dependent. With the ApproxTimeEvolution(H, t, n) method, I am able to prepare the circuit by inputing the Hamiltonian H and time t (and order of Trotter n). But the Hamiltonian is only allowed to be defined with fixed coeffs and Pauli terms.

For example: H = qml.Hamiltonian( [1, 1, 0.5], [qml.PauliX(0), qml.PauliZ(1), qml.PauliX(0) @ qml.PauliX(1)] )

I hope the qml.Hamiltonian can allow time-dependent coeffs so that I don't need to define a new H in every time-step, which is time consuming.

For example: H = qml.Hamiltonian( [2*t, 3*t, 0.5*t-5], [qml.PauliX(0), qml.PauliZ(1), qml.PauliX(0) @ qml.PauliX(1)] )

And then this can be used in ApproxTimeEvolution() method

Thanks

Implementation

No response

How important would you say this feature is?

2: Somewhat important. Needed this quarter.

Additional information

No response

[josh146]

Hi @yulunwang! This is a great feature request.

Perhaps we could add something like the following:

obs = [qml.PauliX(0), qml.PauliZ(1), qml.PauliX(0) @ qml.PauliX(1)]
H = lambda t: qml.Hamiltonian([2 * t, 3 * t, 0.5 * t - 5], obs)

@qml.qnode(dev)
def circuit(t):
    qml.TimeEvolution(H)
    return qml.expval(qml.PauliZ(0))

where H is a function that takes a single parameter (t) and returns the Hamiltonian at that time value.

We could then support some approximate decomposition in order to support this on hardware, perhaps via discretization?

[PabloAMC]

Hi @yulunwang, perhaps this is a bit late now, but there is an even more performant option, based on so-called commutator-free quasi-Magnus operators. Check this repo for an example of how to use Pennylane to simulate time-dependent Hamiltonians https://github.com/XanaduAI/CFQMagnus/blob/main/CFQMagnus/pennylane_simulation.py