Some Last Minute Comments on Qubits 101

[amopremcak]

Latest document looks great! Below is my "1 am" stream of consciousness:

1. In equation (2), R_K is not defined until much later in the document (page 10 I think).

2. In equation (8), \omega_0 is introduced but the symbol \omega_{LC} is introduced in the previous section to refer to the same thing.

3. There are a few times throughout the document where the dependence of coupling on the mode impedance is discussed. The two examples that come to mind when I read this are: (i) for a transmon, C is fixed and so the only way to vary Z_{LC} is by changing L which also changes \omega_{LC} and (ii) for high-kinetic inductance resonators, L goes way up so to maintain the same \omega_{LC}, C must go way down which increases Z_{LC}. I'm not sure if this is worth integrating into a footnote, but are these the cases you had in mind?

4. In section 3.1, the simple derivation uses a symbol V_q which is implicitly defined through the last equality on the rhs on the unnumbered equation of that section.

5. Fig. 2 is missing the symbol R_d as in Fig. 1

6. In section 3.2, the sentence that starts with "Just as we did for the capacitive drive..." uses a two instead of a to. In the sentences that follows there is a "wnder" instead of an under.

7. I am assuming the missing L_a and L_b in Fig. 3 were intentionally left out? Same question for Fig. 4 except about C_a and C_b.

8. In section 5, the symbol \omega_a is used to refer to the qubit frequency with regard to equation (25). I think \omega_q was meant to be used.

9. In the last sentence of section 5, there is a "Noet" instead of Note.

10. I could be making this up, but I believe our fields convention for the raising and lowering operators differs from a lot of other places. It could be worth defining them in terms of outer products to avoid any potential confusion.

11. In section 5.3, the subscripts a & b on the \sigma terms were dropped. Not sure if this was intentional, but a different convention was used in section 4.1-4.2 to discuss qubit-qubit interaction terms.

12. I will send you a dope way to write equation (37) tomorrow but I am too tired right now and need to go to bed.

13. After section 6, the symbol Z_q is used to talk about the qubit's impedance. I see why you didn't decide to reuse Z_{LC}, but it could be worth noting their equivalence so people know how to compute it.

14. In section 6.3, the symbol R_e is introduced to discuss the external line resistance. Perhaps it is worth using R_d since it was used in sections 3.1-3.2 and in Fig. 1-2 to refer to the same thing.