Fix citation and explanation in Floquet calibration example

[balopat]

The Floquet calibration notebook's connection to our research needed more explanation. There is connection to both the quantum ring paper and the Fermi Hubbard paper. I also explained the motivation behind using segments on the line and added a quirk circuit to demonstrate the evolution of the charge density on a 5 qubit segment.

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[balopat]

cc @rmlarose

[MichaelBroughton]

LGTM. You could leave both references in , since they both talk about floquet calibration.

[rmlarose]

IIRC we wanted to reference https://arxiv.org/pdf/2012.00921.pdf for that section because the benchmark circuit in the tutorial is the same as the one in the paper (see Fig. S3) except the tutorial has open boundary conditions and the paper has closed boundary conditions. It's less clear to me how the circuit in the tutorial corresponds to the Fermi-Hubbard experiment, but if I squint I can kind of see it. Either way if @mrwojtek prompted the change this LGTM.

I do like @MichaelBroughton's suggestion of referencing both papers, perhaps at the end of the tutorial ("For more on how Floquet calibration works, see...")

[mrwojtek]

The discussion with Balint started because of the error mitigation techniques that are present in the tutorial, they are closer to the ones in https://arxiv.org/pdf/2010.07965.pdf. However, the Hamiltonian there is more complicated and as you're saying Ryan you need to really squint to see it. The https://arxiv.org/pdf/2012.00921.pdf realizes exactly the Hamiltonian in this tutorial up to a boundary conditions (although in that paper the Hamiltonian is mentioned briefly in the text only).

I think what we really need is a sentence that the technique of averaging over many realizations is included in https://arxiv.org/pdf/2010.07965.pdf. The https://arxiv.org/pdf/2012.00921.pdf is better in terms of physics of this experiment.

[balopat]

Thanks for the comments. I am using this tutorial for a presentation and I wanted to understand the model we are using, and as it was, I found it confusing regarding the connection to the quantum ring paper: we had segments that were not connected by two-qubit gates, there were no single qubit gates between the sqrtISWAPs, I saw no mentioning of z densities. I reached out to @mrwojtek and he explained it from the Fermi-Hubbard (FH) point of view, which made more sense. But now I see the connection to the quantum ring (QR) paper too. And especially that both use Floquet calibration we could keep both in.

I'll rephrase:

• the physics model could be looked at as a simplified version of either of the papers, with some explanation regarding the connection - FH with U=0, fixed theta to sqrtISWAP, single site excitation initial state, single chain; QR with open boundary condition, no complex hopping (hence no Z rotations between the sqrtISWAP gates)
• it measures charge density which is closer to FH paper than the QR paper's Fourier transforms and spectroscopy direction
• it uses post-selection that is in the FH paper and is not present in the QR paper
• it runs the experiment segment_length/line_length times in parallel, and uses averages to smooth out heterogeneity on the chip - though the averaging technique was implemented in the FH paper across 16 different configurations, it was serial, not parallel

[balopat]

Please have a look again @rmlarose @mrwojtek @MichaelBroughton at the update. Thanks!

[rmlarose]

Thanks for the comments! Makes sense and the latest changes look great! I like in particular linking to the quirk circuit.

[mrwojtek]

single electron => single fermionic particle

quirk circuit is cool! Could you place the excitation in the middle (on the 2nd qubit, this is how it's being done in the tutorial).

Otherwise LGTM!

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[balopat]

Sounds good, I'll add those changes in!