Nonlinear dependence on control parameter

[will-atom]

Is it possible to define a nonlinear dependence on a control parameter?

For example, I might create a Hamiltonian function
hamiltonian(H0, (H1,\epsilon))

But I would like to have another contribution (H2,\epsilon^2). Of course I know that this is not possible exactly as I've written it here, because \epsilon is a function of time.

What would be the best way to implement this dependence?

[goerz]

Yes, it should be pretty straightforward in principle:

julia> using LinearAlgebra

julia> using QuantumControl: hamiltonian

julia> using QuantumControlTestUtils.RandomObjects: random_matrix

julia> using QuantumControl.PulseParametrizations: SquareParametrization, ParametrizedAmplitude

julia> using QuantumControl.Controls: get_controls, evaluate

julia> N = 10;

julia> H0 = random_matrix(N; hermitian=true);

julia> H1 = random_matrix(N; hermitian=true);

julia> H2 = random_matrix(N; hermitian=true);

julia> ϵ(t) = 0.5;

julia> a = ParametrizedAmplitude(ϵ; parametrization=SquareParametrization());

julia> H = hamiltonian(H0, (H1, ϵ), (H2, a));

julia> get_controls(H)
(ϵ,)

julia> norm(Array(evaluate(H, 0.0)) - (H0 + 0.5 * H1 + 0.5^2 * H2))
0.0

Except that there was a bug #43, which I just fixed.

Can you work with the current master branch of the JuliaQuantumControl packages? Otherwise, I have make a new release (there's been a few accumulated changes). I could probably do that tomorrow.

[will-atom]

I'm not in a huge rush, thanks for this! Happy to use it on master whenever you release the changes.

[will-atom]

Is it possible to have ϵ also be a ParametrizedAmplitude in this situation? For example to impose a shape.

[goerz]

Yes, of course. You can put in whatever amplitudes you want.

[goerz]

More generally, I would also point you to the section on Arbitrary Generators (again, for the current master, the check_… routines haven't been released yet).

[will-atom]

Thanks very much!

[goerz]

You should be good to go now if you're running QuantumControl 0.8.0.

If you end up with a nice example notebook for this, I wouldn't mind adding it to the documentation and tests in some way. Let me know.