Single Charge Bases + DiagDevice

[shoumikdc]

Adding some small fixes to the single charge basis of the transmon - in particular, we now have three separate single charge bases (full, even, odd). With this, I think the single-charge basis is fully fleshed out.

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Also added a DiagDevice. The whole point of qcsys is to pipeline diagonalizations via nested functions (i.e. JAX style). However, this means that any time we diagonalize a System, we are also diagonalizing each subsystem first. That is, simply calling qubit.get_H() involves diagonalizing a N_pre_diag-dimensional matrix. If N_pre_diag for each subsystem is large (e.g. >1000), then this gets very slow when working with systems.

My proposed solution is to diagonalize each subsystem once and save the resulting (truncated) eigenvalues to a file (e.g. npz). Then, we can create a new DiagDevice, whose Hamiltonian is diagonal and is already written in the energy eigenbasis. This class has a get_H() method, so it is compatible with other devices. This will speed up the construction of composite system Hamiltonians, since instead of having to rediagonalize each subsystem, we can just use the stored data.

[The specific use case where this is highly advantageous is when we want to sweep the coupling between two fixed subsystems, e.g. H_total = H_a + H_b + g_ab * H_int where we sweep g_ab]

[Phionx]

Hm, this seems against the functional paradigm of JAX. Let's discuss tmw.