QCJC: Kannan 2020

I’m not sure if you can tell, but I’ve been recently starting to move away from reading “seminal” papers, and instead working through the new, hot papers of today. I suppose that one danger of doing so is that it’s harder to see if the individual papers that I read will pan out to be an actual game changer or not, whereas the papers from a decade ago have already (partially) withstood the test of time. However, it is life on the cutting edge that is more exciting – more area to explore, question, and discover!

This paper from the Oliver group at MIT explores a new topological way to use superconducting qubits for quantum simulations. Although we are still squarely in the superconducting space, the title, as well as much of this paper, takes inspiration from the atomic nature of these superconducting qubits. Primarily, the fact that superconducting qubits in a microwave waveguide resonator act very similarly to atomic qubits interacting with some wavelength mode. Typically, we see the atom as being much smaller than the wavelength that it is interacting with. However, for these “giant atoms” (which I cannot tell if they are actual things in AMO physics or not?), they are so large that they interact with multiple peaks of the wave at the same time. In this superconducting landscape, exactly where these qubits interact with the waveguide can then be carefully controlled, creating this beautiful braiding pattern shown in Figure 1c, d, e. Instead of the qubit being strictly interacting with the waveguide at a single junction, there are multiple ports to consider, which these authors claim can be used and tuned to protect the qubits even further.

The key idea that is brought up in this paper is that the photons in the waveguide cavity will experience a phase shift that depends on the resonant frequency of the qubit. Since this group is using tunable transmon qubits here, this can be a fairly easily adjustable parameter. The theory then supports that the relaxation rate of the qubit strongly depends on the phase of that photon, leading to the plot in Fig. 2b. The authors argue that when \phi = \frac{\pi}{2}, the qubits are maximally decoupled from relaxation into the waveguide. However, instead of the usual corresponding trade-off of having slower gates, there is still “strong physical couplings to the continuum of modes in a waveguide”.

The justification for this seems to primarily be in the braided design of these giant atoms. In a typical small atom, the interaction strength is proportional to \sin(\theta / 2), where \theta is the phase delay of a photon from one qubit’s coupling point to another qubit’s coupling point. However, in the braided configuration, there are multiple coupling points. Given that the two qubits have uniform coupling strengths to the waveguide, the expression simplifies to that of Eq. 5. At the minimal decoherence point of setting \phi = \frac{\pi}{2}, the interaction strength is directly proportional to \gamma.

This seems to pose a few interesting questions – namely, what would the interaction strength look like for braided giant atoms that are not symmetric in this way? Could you engineer a different interaction strength relationship in that case, and if so, could you actually amplify the signal in some way? However, the symmetry of the current system does seem to make it become much more simple to analyze, which has all of the benefits associated with that.

In fact, the authors go on to engineer two slightly detuned qubits, such that the decoherence-free frequency for each qubit was separated by 720 MHz, allowing the qubits to not only be protected from the environment, but also from each other. It’s a little less clear to me the purpose here – are they planning on tuning the qubits to then move closer to each other only during swapping gates, or just accept that there will be slower exchange rates? It does appear that they are able to achieve exchange excitation rates of 735 kHz, but I don’t really have a good intuition as to if this is good or bad.

In general, I think the bigger picture of this idea – of using giant atoms that are braided together – sounds like it has a vast amount of stuff to be explored. Right now, the two qubits are braided together in the most simple configuration. But what about three qubits? Or four? The number of knots that can be formed – especially if you use some kind of 2.5d geometry – seems incredibly vast. If there is a different error syndrome that can be prevented for each braiding pattern, then weaving together different braided atoms might create a fairly robust structure.

I think my main continued question at this point is how the qubits are different from normal transmon qubits, if there is any difference at all. It seemed to me from Figure 1 that they are just using normal transmons and hooked additional 50-Ohm terminated resonators on each side. Is there some limit to the number of points that a single transmon can be connected to as a giant atom? Is there more sensitivity to asymmetric flux noise from either of the two pathways?

Source: Kannan et. al Waveguide Quantum Electrodynamics with Superconducting Artificial Giant Atoms Nature 583 775 (2020)

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