CQED understanding superconducting qbits circuits

[maajdl]

TL;DR Summary

modeling qbit circuit

I have read a little about cqed, "circuit quantum electrodynamics".
I would be interested in references to dig a qbit deeper in this topic!

I have seen lumped circuit diagrams for superconducting qbits.
The correspondance between classical and quantum models for these circuits is really interresting.
I have seen physical diagrams for how q-circuits are actually implemented.
The correspondance between these diagrams is not so obvious.

I would like to know more about how q-circuits are actually built
and how they could then be modeled or simulated or understood as lumped q-circuits.
I would especially like to understand in detail how the coupling works for setting the state or for reading the state.
For example, I have seen that micro transmission lines (resonators) are involved and I would like to know the principles of their physical modelling.
For example: do their shape matter or does only their length matter?

I guess it is essentially based on a classical model that is later quantified.
So in a sense, it is the classical models of these cicruits that matter first for my understanding.

Any references welcome!

 

[anuttarasammyak]

I find a review in 2020 by web search
https://www.annualreviews.org/doi/10.1146/annurev-conmatphys-031119-050605
I hope you would find one of your taste in the web. If you need more detailed information I recommend you to go to referred papers or contact university or company experts. They would welcome ambitious young people to join the quantum engineering forces.

 

[f95toli]

The "original" circuit QED paper by Blais et al from 2004 is still a good reference.
There are lots of review articles (most available on the arXiv) including a recent one from some of the people who did the initial work
https://arxiv.org/abs/2005.12667

Another good resource is the Qiskit YouTube channel (Qiskit is IBM's quantum software framework) as well as the documentation for Qiskit Metal (which is a free design software for CQED circuits, although you also need a HFSS license to get the most out of it)

About your second question: CQED circuits are in terms of their EM behaviour really just "normal" microwave circuits albeit made using (mainly) superconducting conductors plus some non-linear elements (Josephson junctions).
Hence, the design flow is very similar to what one would typically use for any other MW circuit (say a telecom filter) : You usually would start by a lumped element version of the circuit you need and then you would start designing MW versions of each element: an LC resonator might be implemented as a quarter wavelength resonator, an inductor as a squiggly line etc
All of this design work is mainly done using conventional microwave software. Although increasingly some of the modelling and design is now done using specialised packages such as the aforementioned Qiskit Metal