Publication: Flux qubits and readout device with two independent flux lines

This paper contains the major results of my graduate research so far, compressed into four pages. Instead of the abstract I’m posting something closer to a layman’s explanation, which is below the fold since it got a bit long.
Flux qubits and readout device with two independent flux lines
B. L. T. Plourde, T. L. Robertson, P. A. Reichardt, T. Hime, S. Linzen, C.-E. Wu, and John Clarke
Phys. Rev. B 72, 060506(R) (2005)

Sort-of non-technical explanation: Many of the weirder effects of quantum mechanics don’t show up in macroscopic objects due to a kind of averaging out that occurs when large numbers of atoms are involved. One of these, known as coherent superposition, is the effect described in the famous Schrödinger’s Cat thought experiment. If a physical system has several possible states, mathematical combinations of these states are also available to it: so in the case of Schrödinger’s cat, the states “alive” and “dead” can be combined into coherent superpositions such as “alive” + “dead” and “alive” – “dead”, in which the cat is simultaneously alive and dead. In the case of an actual cat, however, the superposition state would disappear due to the averaging-out process I mentioned, which is referred to as decoherence. The time required for decoherence to take place for a system like a Schrödinger’s cat would be vastly shorter than any observable time.
What we did in our experiments was to build a macroscopic electrical circuit that behaved like a quantum object, with decoherence times long enough that we were able to see quantum effects. The circuit in question was a loop of aluminum, broken in three places by thin layers of aluminum oxide (which in crystal form is sapphire). The circuit was cooled to a temperature 0.04 degrees Kelvin above absolute zero, which is well below the temperature at which aluminum becomes superconducting, losing all resistance to the flow of electricity. One of the wonderful things about superconductors is that electrons condense into a single quantum state, so it becomes a much simpler system with the potential for long decoherence times. The three breaks in the aluminum loop form Josephson junctions in the superconductor, which allow us to control the electrical properties of the circuit.
In order to prove that this was really acting like a quantum object, we had to show that we could make coherent superposition states. Two basic states of the circuit are currents travelling around the loop, either clockwise or counterclockwise. By adjusting the magnetic field applied to the loop (when the field is summed over the loop this is referred to as the flux in the loop), we can make one type of current flow energetically favorable, so that currents flow in just one direction. But we can also balance the flux so that clockwise and counterclockwise currents have the same energy (this is called the degeneracy point). In that case, the system will naturally form coherent superposition states like CW + CCW and CW – CCW. It turns out that, while the CW and CCW states have the same energy, the combinations have different energies depending on whether they are added or subtracted from each other. This allows us to detect the superposition by applying microwave radiation with energy equal to the energy difference between the two states; when the circuit is in the lower energy state it will absorb the radiation and switch to the higher energy. We looked at the radiation absorbed by the circuit as the magnetic flux was varied across the degeneracy point: on a plot of radiation frequency vs. magnetic flux, an incoherent system will show straight lines going down to zero when the current flows are balanced, but a coherent system will bend away from zero frequency as it forms superposition states. Here’s what we saw:

Not only did we see the bending of the curve away from zero, we were able to measure the energy difference between the two coherent superposition states, based on the observation that the lowest radiation absorbed was at a frequency of 4 GHz. The next step was to show that we could create coherent superpositions even at points when they aren’t energetically favorable. This is done by sending short pulses of radiation, which cause the circuit to oscillate between CW and CCW current states, passing through superpositions of the two states as it does so. These are known as Rabi oscillations, and they fade away as the system loses its coherence, so this also gives us a measurement of the decoherence time. This is one of our Rabi oscillation measurements:

As you can see the oscillations disappear in are significantly smaller after about 80 nanoseconds. We’d like this time to be a lot longer, which brings me to the question of what the purpose of all this is. This connects to quantum computing, a hot topic in physics based on the idea that computers can do certain calculations much faster if they can manipulate quantum superpositions of numbers. The basic element of a quantum computer would be a quantum bit, or “qubit”, which like a classical bit would have “0” and “1” states but could also form superpositions of these states. The circuit I’ve described here is an example of a qubit, known as a flux qubit since it uses the magnetic flux in the loop. There are a number of different approaches being investigated for quantum computing, but one advantage of using superconductors is that the qubits can be produced on a chip using existing semiconductor technology, and scaled to a system with many qubits relatively easily. Several groups around the world are currently working on flux qubits, and we are not the first to achieve results like these. Our qubit is distinct from the others in a few ways: it is quite a bit larger than other implementations, and the magnetic field is applied to it from a coil integrated onto the chip, which is important for scalability. Whether this route will be practical for quantum computation has yet to be determined, of course, but that’s more of a problem for the engineers. (Feynman would say that we are already doing engineering…)
Anyway, I hope this explanation was illuminating and/or interesting. In the past I’ve just posted the abstract, which tends to be a bunch of meaningless jargon to those outside the field.
UPDATE: I have posted a follow-up on decoherence issues here.

23 thoughts on “Publication: Flux qubits and readout device with two independent flux lines

  1. Mason

    The layperson’s explanation seems good to me, but I kind of qualify as being part of the “general physics audience.”
    By the way, I think something that could be very cool would be to take this explanation of what you’re doing, expand it a bit with layperson’s explanations of background stuff (more about Rabi oscillations and Josephson junctions, etc.), and submit it to American Scientist. I think that that would be a great fit for that magazine. They will edit the Hell out of what you submit, but I think this is something they’d like a lot.

  2. Lemming

    You realize I can’t read “Josephson junction” without twitching just a little bit?
    I take minor offense to the following:
    “As you can see the oscillations disappear in about 80 nanoseconds.”
    Well, not so much offense as it is that it just leaves me wondering what metric I’m missing that would tell me the difference between oscillations being apparent and “disappear”ing. But I digress!
    This is really cool though. I’m still a bit of a pessimist regarding whether or not it’ll ever be possible to build quantum computers that scale, but I’m only slightly educated on the matter and would love nothing more than to be proven wrong.

  3. Arcane Gazebo

    Oops. Yeah, I should rewrite that 80 ns statement. I was trying to translate from “The 1/e decay time of the oscillations is 80 ns” but that statement is a bit strong.

  4. Mason

    I am pessimistic about quantum computers ever being realized (and that includes the BEC in optical lattice or superlattice approach to which some of my research pertains), but plenty of cool (and likely useful) stuff has been found from quantum computing research and plenty more cool stuff will be as well. (This, of course, follows a long tradition in science.) Also, there are plenty of people doing research in quantum computing who believe similarly about the ultimate success of the current long-term goals.

  5. Arcane Gazebo

    Let me state my total confidence in the realization of quantum computing, and my absolute conviction that flux qubits are a superior architecture, and that these opinions have nothing to do with the grant proposal that is pending approval and the remote possibility that the funding agencies might find this thread.

  6. Mason

    Heh, I don’t currently have a proposal pending. :)
    It is quite interesting to compare what people say to what they write in their grant proposals.
    Correct me on the particular technologies if I’m wrong (because there’s a good chance I’m getting the details wrong) but very important current stuff like our wireless technologies were side roads on very well-funded research into other stuff that never panned out. That’s the road I envision for quantum computing. (Lots of nice math, philosophy, and foundational physics [which are correlated] has come out of this already, and I expect we’ll eventually see something practical too—just not a quantum computer.)
    Personally, I’m rooting for the BEC implementation. :) I don’t currently have a grant proposal pending, but I will. (The deadline is 2 months away, so I haven’t started revising last year’s version yet.)

  7. Mason

    Errrr…I mean just not a quantum computer usable for practical things. I know people have been able to use them to factor 15. :)

  8. Chris LS

    As I often tell my wife, I look at stuff like this, and my mind tends to tell me it says, “blahblahblah blah blahblah blahBLAHblah BLAHAHAHA”.
    Of course, if I actually took the time to read it carefully, I’m sure it would be fascinating. *8)

  9. Mason

    Travis, I’m serious about expanding this for American Scientist (or an equivalent venue). You’ve obviously shown you can write for a layperson’s audience (which is really hard to do) and you’ve already done the hardest part of the work—describing the current research in understandable terms as opposed to describing background material in such terms.

  10. Arcane Gazebo

    Kyle: I’ve been thinking lately about ways to blog the day-to-day stuff. I’d like to be writing more about the process of experimental science, both as an outreach type of thing and because I think it could be interesting.
    Mason: I’m seriously considering this.

  11. Maynard Handley

    Screw the quantum computing stuff which is of zero interest to me. Focus on the decoherence. Do we have any theory yet of what is driving this? Penrose hypothesizes (but admits he has no evidence, just a suspicion) that it’s hooked into curvature of space-time, but this is the only physics argument (as opposed to “at this point a miracle happens” arguments) that I have ever seen. If we don’t have a theory, do we at least have a set of useful data points — eg the coherence time varies in this way depending on these parameters?

  12. Arcane Gazebo

    In superconducting qubits we tend to look for more mundane sources of decoherence. Any source of noise in the environment that couples to the qubit is a potential culprit, and we are able to predict what decoherence rates to expect based on a given noise spectrum. The typical calculation uses the “spin-boson model” (due to Leggett) which models the noise source as a collection of harmonic oscillators coupled to the qubit. The most likely dominant source of noise in our experiment is electrical noise from our electronics which acts on the qubit via our readout device. We are currently gearing up for some experiments to test this.
    Another experiment we did was to crank up the repetition rate on our measurements, which injected a lot of heat into the sample. We saw an increase in decoherence rates due to this, and were able to model it very successfully as quasiparticle and phonon coupling to the qubit. One of the nice things about the result is that we really had a knob we could turn (i.e. the speed of the measurements) to move the decoherence rates up or down.

  13. Maynard Handley

    So does this mean, that, in a hand-waving sense, the source of decoherence in your system is more “classical” than quantum, and so tells us nothing essential about “the collapse of the wave function”?

  14. Arcane Gazebo

    I wouldn’t say that. If the source is quasiparticles or phonons, it really is quantum, as these are quantum excitations. (Our model of this effect is probably semiclassical.) Likewise if the source is nuclear spins in the aluminum, which is another possibility we’re considering.
    I’m not sure what that distinction has to do with the collapse of the wavefunction. (On the other hand, I’m not really up to speed on QM interpretations and philosophy, either.) There’s not really any kind of collapse going on as I understand it, rather, the qubit originally contains phase information, but interacts with a large number of oscillators with random phases in the environment, so that the original phase information gets dispersed in the environment as the qubit becomes entangled with it. But maybe I am misinterpreting your question.

  15. tplaine

    Are you considering experiment with qubit coupled to harmonic oscillator (for example like Delft or Yale)?

  16. Mason

    Heh, I think Travis has set a record for largest number of posts on one topic. It just goes to show: Everybody loves physics. (Maybe not physicists, but at least they love physics… :) )

  17. Arcane Gazebo

    Kyle: Good point, I could probably do a follow-up post if I get a few minutes today.
    tplaine: Not at present (although those are beautiful experiments!); right now we are focused on implementing the two-qubit coupling scheme we describe in B.L.T. Plourde et al., Phys. Rev. B 70, 140501 (2004).
    Mason: This, the 23rd comment, ties the previous record-holder, which was the open thread that ran on Election Day last year. The qubit post benefited from a link by the mighty Brad DeLong, whose readership is larger than mine by a factor of 10^x.

Comments are closed.