Thursday, May 21, 2015

dropping my work on the arXiv

My first quantum computing manuscript having been recently dropped on the arXiv, the venerable library of math and physics preprints, gives me a chance to discuss some of what I spend my days doing. I work on building a quantum computer using superconducting qubits (quantum bits), a subject that is more or less an amalgamation of stolen ideas from three disparate fields. Two of these, the use of Nuclear Magnetic Resonance (NMR, think of the MRIs that image you in the hospital (the 'N' was dropped due its perceived lack of wholesomeness)) for pulsed control techniques and Superconducting Quantum Interference Devices (SQUIDs, sensitive detectors of magnetic fields and also used in medical imaging) for superconducting device design and fabrication will have to wait for another day. For my paper is a further derivation from the ideas taken from atomic physics.

The original co-opting of atomic physics ideas came from the Yale group in 2004. Seeking better protection of the information stored in superconducting qubits from 'leaking' out to the environment, they looked to cavity quantum electrodynamics (CQED) of atomic physics. Simply put, a cavity (hollow metal box) imposes boundary conditions on the electromagnetic modes that can exist within it (like the vibrations of a stringed musical instrument are defined on one 'boundary' by your finger). If you put an atom inside that cavity, its rate of spontaneous decay from the excited state to the ground state is modified by those boundary conditions, depending on how suppressed/enhanced radiation at the decay frequency is. For example, the lowest frequency of a cavity is called its fundamental harmonic (just as the string instrument). If the fundamental harmonic frequency is the same as the atomic decay frequency (of the emitted photon), spontaneous decay occurs faster than it would if there was no cavity. However if they differ in frequency (the atom is detuned from the cavity), its spontaneous decay occurs at a much lower rate. This observation of Edward Mills Purcell was formulated in perhaps the most cited abstract of all time. The Yale group applied this idea to the analogue of CQED in these two papers, and called it circuit QED (cQED). Instead of the hollow metal box, the cavity is a coplanar waveguide transmission line resonator (hammer the coax piping you Game of Thrones into two dimensions and you’ve got the right idea), and instead of an atom, use your superconducting qubit. The fact that you can effectively design the interaction strength and frequency of these pieces while understanding much of it in terms of basic circuit theory gives you the lowercase 'c'. A big added bonus here is that the state of the qubit (ground or excited) changes the effective frequency (or phase) of the cavity, allowing you to indirectly extract the information, at a frequency detuned from the qubit’s.

Taking this to the next level, you want your cavity to ‘leak’ photons rapidly, because the photons carry the qubit information and want to do fast measurements because you're busy and all, but when you design the cavity to be leaky you also decrease the qubit lifetime (T1, inversely proportional to the spontaneous emission rate).  A good way of fixing this problem is to explicitly filter radiation at the qubit frequency, since you’re already measuring at a different frequency (the cavity one) anyway. And this has been done by a couple of research groups already: add a microwave filter to your device and voila! Some of the problems with this, though, are that microwave filters take up a lot of space (usually one fourth or one half of the wavelength of the cavity or qubit, which adds up to a number of millimeters). Also you might take a hit on your readout rate. My manuscript introduces a similar idea, however presenting the filter as a small capacitance in the form of a small crosstalk between the qubit and the environment (thereby necessitating a negligible amount of space).

Bound on qubit lifetime due to spontaneous decay to the electromagnetic environment. The dip around 6.4 GHz is the cavity frequency at which the state of the qubit is read out. The peaks on the left are due to the action of the filter, predicting qubit lifetimes could exceed 10s of milliseconds (~ 3 orders of magnitude higher than currently observed for this QC paradigm).
[NT Bronn et al, arXiv:1504.04353]

The manuscript is relatively long (for a physics paper, that means > 4 pages), for the purpose of being self-contained, so that casual readers that understand circuit theory can appreciate the concept, with the important physics-y equations explained early on, and then on only discussed in observable quantities. The idea of the paper comes from the cavity, which essentially can be thought of as a parallel LC (inductor-capacitor) resonator, having a maximum impedance to ground at its resonant frequency, in the electrical engineering parlance. But if the LC resonator was in series, it would have a filtering effect (because it would act as a short to ground). So combining a capacitor (or inductor) in series with the resonator offers a subcircuit that passes at the 'information' (cavity) frequency but filters at the 'qubit' frequency. The next step is realizing the large capacitor it would take to make this thing useful can actually be obtained using some old-fashioned electrical engineering that’s over a hundred years old, the good old Y-Δ transform. Then the capacitor becomes such a small one as to almost be unavoidable, so much so that electromagnetic simulations need to be performed to figure out exactly how to design it. We then spend a lot of time and equations showing that this filter can be used to do fast measurements with a tiny amount of error.

So that's the Cliff's Notes version, and I wouldn't want to spoil the ending (just kidding... that's about it). But also, we've summarized a fair amount of work that's been done over the past decade in one convenient place, brought in an alternative view of it, in a such a way that I can only hope will maximize citations.