Tunable superconducting flux qubits with long coherence times

In this work, we study a series of tunable flux qubits inductively coupled to a coplanar waveguide resonator fabricated on a sapphire substrate. Each qubit includes an asymmetric superconducting quantum interference device which is controlled by the application of an external magnetic field and acts as a tunable Josephson junction. The tunability of the qubits is typically $\pm 3.5$ GHz around their central gap frequency. The measured relaxation times are limited by dielectric losses in the substrate and can attain $T_{1}\sim 8 \mu s$. The echo dephasing times are limited by flux noise even at optimal points and reach $T_{2E}\sim 4 \mu s$, almost an order of magnitude longer than state of the art for tunable flux qubits.
Comment: Supplementary Materials is at the end of the file