Slight issues on tutorial 4.

[fretchen]

In tutorial number 4 the gate is defined through the Hamiltonian:

H_{\text{OAT}}(\chi, \Delta, \omega) = \sum_{i=1}^3 \chi_i L_{z, i}^2 + \Delta_i L_{z, i} + \Omega_i L_{x, i}

However, in the gate chi Delta and Omega are also used as the angles, which should be the product no ? So I wonder about the proper definitions here ...

[fretchen]

I also attempted to implement the ly gate, however the collective_spin_simulator throws the error that rLy is not implemented. Is this a bug or a feature ?

[LaurinFischer]

• To your first point, the "angles" in the gate refer specifically to that Hamiltonian, so the gate generated by this Hamiltonian picks up the same definitions. I'm not sure what you mean by taking the product of these parameters?

• To your second point, the collective_spin_simulator is a specific example of a spin backend which already has a fixed gateset defined in its configuration, mocking the restrictions of a real hardware backend. These can be looked up through the supported_instructions of the backend configuration and currently include

"supported_instructions": [
    "rLz",
    "rLx",
    "rLz2",
    "OAT",
    "rLzz",
    "measure",
    "barrier",
],

You would need to add your rLy gate there or simply use the general SpinSimulator backend which does not have any restrictions on the gates it can process.
Hope this clears things up.

[fretchen]

• Concerning the first point:
  Well the gate is U = e^{itH} right. So the parameters of the Hamiltonian are fixed, but the angle in front of the operators changes as time moves. Take for example the simple case of the U = e^{it \Delta Lz}. Delta is fixed in the experiment, but the time changed, so the thing that should be given to the unitary is t\times \Delta...

• Good to know for the second point.

[LaurinFischer]

Back to your first point:
Is see what you mean, but I'm not sure there's a good solution for this.
In the circuit we don't care about experimental parameters and gate times but only the resulting angles which is given by the abstract parameters (in the case of single spin rotations). And, frankly, we need some names for the parameters in the gate. We chose chi, Delta, Omega to hint at the standard notation of the Hamiltonian, not because these correspond to the actual experimental values.
So if that is confusing from the experimental point of view, what other name for the parameters would be natural?

(You can also think of it as setting t = \hbar = 1 (dimensionless) for the purpose of the gate definition. )

[fretchen]

So if that is confusing from the experimental point of view, what other name for the parameters would be natural?

Something like another greek letter would be great. But in the FH model, the variable J and U are really associated with fixed parameters. It would hurt my AMO/condensed-matter etc eye much less to see: \theta_J = Jt than J = Jt...