Micromachined Integrated Quantum Circuit Containing a Superconducting Qubit

We present a device demonstrating a lithographically patterned transmon integrated with a micro-machined cavity resonator. Our two-cavity, one-qubit device is a multilayer microwave-integrated quantum circuit (MMIQC), comprising a basic unit capable of performing circuit-QED operations. We describe the qubit-cavity coupling mechanism of a specialized geometry using an electric-field picture and a circuit model, and obtain specific system parameters using simulations. Fabrication of the MMIQC includes lithography, etching, and metallic bonding of silicon wafers. Superconducting wafer bonding is a critical capability that is demonstrated by a micromachined storage-cavity lifetime of 34.3 mu s, corresponding to a quality factor of 2 x 10(6) at single-photon energies. The transmon coherence times are T-1 = 6.4 mu s, and T-2(echo) = 11.7 mu s. We measure qubit-cavity dispersive coupling with a rate chi(q mu)/2 pi = -1.17 MHz, constituting a Jaynes-Cummings system with an interaction strength g/2 pi = 49 MHz. With these parameters we are able to demonstrate circuit-QED operations in the strong dispersive regime with ease. Finally, we highlight several improvements and anticipated extensions of the technology to complex MMIQCs.