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arXiv:cond-mat/0605398

Galvanic coupling of flux qubits: simple theory and tunability

Alec Maassen van den Brink

Published May 16, 2006• 1 citation
arXivHTMLPDF

Abstract

Galvanic coupling of small-area (three-junction) flux qubits, using shared large Josephson junctions, has been shown to yield appreciable interaction strengths in a flexible design, which does not compromise the junctions' intrinsic good coherence properties. For an introduction, I recapitulate an elementary derivation of the coupling strength, which is subsequently generalized to the case of tunable coupling for a current-biased shared junction. While the ability to vary coupling constants by, say, 20% would be useful in experiments, sign-tunability (implying switchability) is highly preferable for several quantum-computing paradigms. This note sketches two ideas: a "crossbar" design with competing ferro- and antiferromagnetic current-biased tunable couplings, and a "mediated" one involving an extra loop between the qubits. The latter is a variation on proposals for tunable capacitive coupling of charge qubits, and tunable inductive coupling of large-area flux qubits.

DOI
10.48550/arxiv.cond-mat/0605398

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Galvanic coupling of small-area (three-junction) flux qubits, using shared large Josephson junctions, has been shown to yield appreciable interaction strengths in a flexible design, which does not compromise the junctions' intrinsic good coherence properties. For an introduction, I recapitulate an elementary derivation of the coupling strength, which is subsequently generalized to the case of tunable coupling for a current-biased shared junction. While the ability to vary coupling constants by, say, 20% would be useful in experiments, sign-tunability (implying switchability) is highly preferable for several quantum-computing paradigms. This note sketches two ideas: a "crossbar" design with competing ferro- and antiferromagnetic current-biased tunable couplings, and a "mediated" one involving an extra loop between the qubits. The latter is a variation on proposals for tunable capacitive coupling of charge qubits, and tunable inductive coupling of large-area flux qubits.
We have realized controllable coupling between two three-junction flux qubits by inserting an additional coupler loop between them, containing three Josephson junctions. Two of these are shared with the qubit loops, providing strong qubit-coupler interaction. The third junction gives the coupler a nontrivial current-flux relation; its derivative (i.e., the susceptibility) determines the coupling strength J, which thus is tunable in situ via the coupler's flux bias. In the qubit regime, J was varied from approximately 45 (antiferromagnetic) to approximately -55 mK (ferromagnetic); in particular, J vanishes for an intermediate coupler bias. Measurements on a second sample illuminate the relation between two-qubit tunable coupling and three-qubit behavior.
We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.
We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.
Superconducting flux qubits are a promising candidate for solid-state quantum computation. One of the reasons is that implementing a controlled coupling between the qubits appears to be relatively easy, if one uses tunable Josephson junctions. We evaluate possible coupling strengths and show how much extra decoherence is induced by the subgap conductance of a tunable junction. In light of these results, we evaluate several options of using intrinsically shunted junctions and show that based on available technology, Josephson field effect transistors and high-Tc junctions used as π shifters would be a good option, whereas the use of magnetic junctions as π shifters severely limits quantum coherence.
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 ${\ensuremath{\beta}}_{Q}$ 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 ${\ensuremath{\beta}}_{Q}$. As ${\ensuremath{\beta}}_{Q}$ is increased beyond 0.50.50.5, the tunnel splitting between the ground and first excited states decreases rapidly, and the device becomes progressively less useful as a qubit.