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arXiv:cond-mat/0501085 · Physical Review B

Direct Josephson coupling between superconducting flux qubits

M. Grajcar, A. Izmalkov, S. H. W. van der Ploeg, S. Linzen, Evgeni V. Il’ichev, Th. Wagner, Uwe Hübner, H.‐G. Meyer, Alec Maassen van den Brink, Sergey V. Uchaikin, Alexandre M. Zagoskin

Published Jul 14, 2005• 57 citations
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Abstract

We have demonstrated strong antiferromagnetic coupling between two three-junction flux qubits based on a shared Josephson junction, and therefore not limited by the small inductances of the qubit loops. The coupling sign and magnitude were measured by coupling the system to a high-quality superconducting tank circuit. Design modifications allowing to continuously tune the coupling strength and/or make the coupling ferromagnetic are discussed.

DOI
10.1103/physrevb.72.020503

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We have demonstrated strong antiferromagnetic coupling between two three-junction flux qubits based on a shared Josephson junction, and therefore not limited by the small inductances of the qubit loops. The coupling sign and magnitude were measured by coupling the system to a high-quality superconducting tank circuit. Design modifications allowing to continuously tune the coupling strength and/or make the coupling ferromagnetic are discussed.
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 first experimental results on a device with more than two superconducting qubits. The circuit consists of four three-junction flux qubits, with simultaneous ferro- and antiferromagnetic coupling implemented using shared Josephson junctions. Its response, which is dominated by the ground state, is characterized using low-frequency impedance measurement with a superconducting tank circuit coupled to the qubits. The results are found to be in excellent agreement with the quantum-mechanical predictions.
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 experimentally confirm the functionality of a coupling element for flux-based superconducting qubits, with a coupling strength JJJ whose sign and magnitude can be tuned in situ. To measure the effective JJJ, the ground state of a coupled two-qubit system has been mapped as a function of the local magnetic fields applied to each qubit. The state of the system is determined by directly reading out the individual qubits while tunneling is suppressed. These measurements demonstrate that JJJ can be tuned from antiferromagnetic through zero to ferromagnetic.
We propose a scheme for tunable coupling of phase-coupled flux qubits. The phase-coupling scheme can provide a strong coupling strength of the order of Josephson coupling energy of Josephson junctions in the connecting loop, while the previously studied inductive coupling scheme cannot provide due to small mutual inductance and induced currents. We show that, in order to control the coupling, we need two dc SQUID's in the connecting loop and the control fluxes threading the dc SQUID's must be in opposite directions. The coupling strength is analytically calculated as a function of the control flux at the coresonance point.
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.