Here’s the latest publication on Clarke group qubit research, which appeared in Physical Review B at the end of May. Normally I give a non-technical explanation in these posts, but this paper is entirely devoted to working out gory technical details. It essentially goes through how to calculate a priori the properties of the flux qubits that I’ve written about previously. This calculation had been done for “small” qubit loops—small being defined in terms of the loop inductance but corresponding to a few microns on a side—our qubits are much larger than this (100 microns) and so we needed to figure out the more general solution.
The vast majority of the work in this paper was done by T. L. Robertson; my primary contribution was checking the math and the Mathematica code.
Quantum theory of three-junction flux qubit with non-negligible loop inductance: Towards scalability
T. L. Robertson, B. L. T. Plourde, P. A. Reichardt, T. Hime, C.-E. Wu, and John Clarke
Phys. Rev. B 73, 174526 (2006)

The three-junction flux qubit (quantum bit) consists of three Josephson junctions connected in series on a superconducting loop. We present a numerical treatment of this device for the general case in which the ratio betaQ of the geometrical inductance of the loop to the kinetic inductance of the Josephson junctions is not necessarily negligible. Relatively large geometric inductances allow the flux through each qubit to be controlled independently with on-chip bias lines, an essential consideration for scalability. We derive the three-dimensional potential in terms of the macroscopic degrees of freedom, and include the possible effects of asymmetry among the junctions and of stray capacitance associated with them. To find solutions of the Hamiltonian, we use basis functions consisting of the product of two plane wave states and a harmonic oscillator eigenfunction to compute the energy levels and eigenfunctions of the qubit numerically. We present calculated energy levels for the relevant range of betaQ. As betaQ is increased beyond 0.5, the tunnel splitting between the ground and first excited states decreases rapidly, and the device becomes progressively less useful as a qubit.

Less than two months remain before the APS March Meeting, which in terms of blogging means more short posts at odd hours, when I’m not in the lab trying to gather lots of last-minute data. Here’s the abstract for my talk:

Abstract: K40.00012 : Variable Coupling of Two Flux Qubits
5:06 PM–5:18 PM
T. Hime, P.A. Reichardt, B.L.T. Plourde, T.L. Robertson, C.-E. Wu, A.V. Ustinov, John Clarke
We report observations of variable coupling of two flux qubits. The qubits are coupled inductively to each other and to a readout Superconducting QUantum Interference Device (SQUID). By applying microwave radiation to the device, we observed resonant absorption in each of the qubits when the level splitting in the qubit matched the energy of the microwave photons. Using the two on-chip flux bias lines we adjusted the bias of each qubit so that the energy levels of the two qubits were equal; we then observed a splitting of the resulting absorption peak characteristic of coupling between the qubits. We varied the coupling between the qubits by changing the current bias in the SQUID in the zero voltage state, thereby changing its dynamic inductance and thus modifying the effective mutual inductance between the qubits. We compare the resulting changes in splitting with our predictions. This controllable coupling should be extendable to many qubits.

I’ll do a post explaining this in more detail around the time of my talk; some of this work is still, uh, “in progress”. (In fact we have performed all the experiments mentioned in the abstract, but we are working on collecting more/better data.) The talk immediately before mine covers some other results from these experiments.