Introduction to superconducting Circuits: Hamiltonian Engineering and the Kerr-Cat Qubit - Q&A

Explore the world of quantum superconducting circuits with Dr. Rodrigo Cortiñas, Postdoctoral Associate at Quantronics Laboratory (Qlab), Yale University

In a recent webinar with Physics Today sponsored by Oxford Instrument NanoScience, Cortiñas discussed the building of classical versus quantum circuits, the Hamiltonian engineering of qubits and how the Kerr-Cat qubit got to “live”.

"In Qlab, we currently have five working cryostats, each housing different research projects. All of them are from Oxford Instruments. Here, we are all strongly driving our systems and that requires a robust cryogenic environment to keep the low temperatures as qubits like the Kerr-cat are born, live and die."

To begin, can you explain to us the difference between making a classical circuit versus a quantum circuit?

I would say that deep down, all circuits - together with the rest of nature - are quantum. It so happens that in most situations found in real life the quantum effects are completely washed away, and what is left is what we know as classical physics. The short answer would be that a quantum circuit is one in which the “non-linearity” overcomes, for a while at least, the dissipation. It is somehow illuminating to see that if the dissipative terms dominate over the non-linear terms in the Hamiltonian the quantum correction will never see the light of day... If what I just said is not obvious, I would say that it is because there is a language gap between the quantum world (usually formulated in Hilbert space) and the classical world (formulated in phase-space). On the other hand, if we bring the quantum operators down to phase-space, then the parallel between the two theories is transparent. The Schrödinger equation becomes the classical Liouville equations plus corrections proportional to powers of! It so happens that the corrections to the Liouville equation are not only proportional to but also proportional to the non-linearity of the Hamiltonian. The final comment might be that when dissipation is introduced (either classically or quantumly), the equation gains terms that scale much like the “quantum corrections”. This is why to make quantum circuits we need to make them out of dissipationless superconductors in dilution refrigerators. Not only that, but the system needs to be extremely non-linear (otherwise you just have a frictionless classical system!). Happily in the realm of superconductivity, we have a dissipationless highly non-linear element: the Josephson junction. Circuits made at cryogenic temperatures including Josephson junctions easily overcome the requirements to exhibit quantum behaviour.

Can you explain Hamiltonian engineering and how it can be applied?

So, you are given these superconducting materials and these Josephson junctions but what are you going to do with them? Well, actually, the amount of qualitatively different systems you can build using so little building bricks is vast. Hamiltonian engineering is usually understood as making hardware that behaves as you would want, with the bricks you have. In quantum computing, for example, we are looking for systems that preserve “well” the quantum information, that are robust to parameter variation, and that can be operated rapidly. Today many of the stones in the way to an all-powerful quantum computer are technological constraints. Hamiltonian engineering, when thinking of qubits, is the task of making new and better systems that will allow for the technological implementation of quantum information processing. Further, there is a very interesting and not yet sufficiently explored direction that is to engineer-driven systems to encode information. This direction is still an active research topic at Yale. In a similar way that an ordinary basketball is only stable over your finger when it is fastly spinning, some otherwise unremarkable qubits become extremely stable when driven. Moreover, in the same way that a driven (Paul) trap for atomic ions achieves something fundamentally impossible for static fields (due to Earnshaw’s theorem), driven quantum circuits can exhibit behaviors without static analog, and they may be the key to overcoming crippling technological limitations. A great example is the Kerr-cat qubit recently developed at Yale.

What is the Kerr-Cat qubit and how did it come to light?

Many of these pets have been around at Yale for quite some time now, and the Kerr-cat is the latest one. These types of qubits are called cats because they are the quantum superposition of “classical” states, reminding us of the cat story made up in the 1930s by Schrödinger. Interestingly, the fable is used to this day to send a lesson: the superposition of classical states is unstable. Regardless of these statements, and thanks to recent technological advancements, the irreverent idea of using cats to manipulate quantum information opened new unexpected and promising directions. The statement might be turned around and say, without eliminating the oxymoron, that the key is in that “classical” states are very stable and that now we can superpose them to do quantum tasks. 

The Kerr-cat in particular is a great example of the development in the understanding of the field... It illustrates i) the interplay between non-linearity and dissipation, ii) hardware Hamiltonian engineering, and more importantly iii) the power of driven Hamiltonian engineering. I can briefly explain myself: i) dissipation is always present, and the non-linearity, as quantum as it may sound, also brings all sorts of collateral problems, so we want enough but not too much, and actually, we wish for so little that the static Hamiltonian would become annoying to work with. ii) To bring the Kerr-cat to life it was required to use a SNAIL transmon, a feat of hardware engineering that provides a rare 3-wave mixing dipole element (also developed at Yale), but importantly iii) it is only by strongly driving the SNAIL that a Kerr-cat is created. And indeed the driven SNAIL housing a Kerr-cat qubit surpasses the corresponding undriven static qubit by orders of magnitude. The bottom line for the quantum engineer is that driving your system allows you to enhance a weak non-linearity avoiding many technical problems. The articulation of these concepts makes driven qubits like the Kerr-cat possible.

How has Oxford Instruments facilitated this important research at Yale University?

In Qlab, we currently have five working cryostats, each housing different research projects. All of them are from Oxford Instruments. Here, we are all strongly driving our systems and that requires a robust cryogenic environment to keep the low temperatures as qubits like the Kerr-cat are born, live and die. We also count on on-site support from Oxford Instruments through our support package. If ever we encounter a problem with one of our cryostats, or if something doesn’t function correctly, we have someone to turn to. It is very educational for the students to have direct interaction with experts in cryogenics and helps them develop the necessary skills to become expert researchers in the field of superconducting circuits. 

For the original Kerr-cat paper, see: Nature 584 (2020) 205-209

Dr. Rodrigo Cortiñas