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arXiv:cond-mat/0605588 · Physical Review Letters

Controllable Coupling of Superconducting Flux Qubits

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

Published Feb 2, 2007• 188 citations

Abstract

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.

DOI: 10.1103/physrevlett.98.057004

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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 experimentally confirm the functionality of a coupling element for flux-based superconducting qubits, with a coupling strength

J

whose sign and magnitude can be tuned in situ. To measure the effective

J

, 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

J

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.

The ability to non-dissipatively tune the Josephson coupling energy of Josephson junctions is a useful tool in frequency-tunable qubits. This is typically done by threading magnetic flux through two junctions connected in a loop, a geometry that exposes the qubit to magnetic environmental noise. In this paper, we show that by biasing a junction with supercurrent from a separate pair of superconducting leads coupled to the device, the Josephson energy can be tuned without the need for a flux loop. Our multiterminal device may enable the realization of a frequency-tunable qubit with greatly reduced susceptibility to flux noise.

The authors propose a qubit-qubit coupling scheme for superconducting flux quantum bits (qubits), where quantized Josephson junction resonator and microwave irradiation are utilized. The junction is used as a tunable inductance controlled by changing the bias current flowing through the junction, and thus the circuit works as a tunable resonator. This enables them to make any qubits interact with the resonator. Entanglement between two of many qubits whose level splittings satisfy some conditions is formed by microwave irradiation causing a two-photon Rabi oscillation. Since the size of the resonator can be as large as submillimeters and qubits interact with it via mutual inductance, their scheme makes it possible to construct a quantum gate involving remote qubits.