Simulating 3 Level Systems

[ArturDomingues]

Hello, I was trying to simulate some hyperfine interactions and I used qiskit nature to define S=1 operator, and when I tried to used the solver method it returned me and error saying that I couldn`t use matrices in that module, what can be done to simulate the interaction between a S=1/2 and S=1 particles? Do I need to define directly the hamiltonian in the S_total_z basis (S_total being the spin of the coupled system)?

[DanPuzzuoli]

Hi!

Do you mean that you tried using the matrices from qiskit nature in dynamics and it raised an error? If so what type are the matrices in qiskit nature? Can you share part of the error message?

[ArturDomingues]

I think I solved my problem. I was using x=SpinOp("X", spin=1) and not x=Operator(SpinOp("X", spin=1)), just this solved what was happening, but I really don't know why. so a explanation would be nice =D

[DanPuzzuoli]

Ah interesting. Taking a look at the class, the reason is that SpinOp (and more generally, the SecondQuantizedOp base class that it inherits from) doesn't have an __array__ method.

This is relevant because of the following:

• Internally, when you construct a Solver or one of the model classes in dynamics, it will attempt to convert all of the matrices you supply into arrays (either numpy, jax, or the Array class). This is true with whatever format you specify, whether they be specified as numpy arrays already, qiskit Operator instances, and even qutip QObj is supported.
• To convert an input matrix x to an array, we call np.array(x). When calling np.array(x):
  • If x is something numpy recognizes (like a list of floats) it'll do its usual thing.
  • If x however is not an instance of a class that numpy recognizes, it will check if x has an __array__ method. If it does, calling np.array(x) will actually return x.__array__(). Basically numpy has provided a mechanism by which, if you write a new class, you can control how np.array(x) behaves.
  • If numpy does not recognize the type of x, AND x does not have an __array__ method, an error is raised.
• That all being said, Operator does have an __array__ method, whereas SecondQuantizedOp does not. Hence, if you pass operators in this format to dynamics it will fail.

(Note that I may not have the details of the operation of np.array 100% correct, but I think the general idea of what I'm saying is right.)

[ArturDomingues]

That explains the outputs of printing x as SpinOp and as Operator. I was having problems doing basic operations like @ or raising x to a power because these aren't implemented in qiskit_nature, thanks for the nice explanation.