This is the published version, also available here: http://dx.doi.org/10.1103/PhysRevB.81.134510.A rf–superconducting quantum interference device (SQUID) flux qubit that is robust against fabrication variations in Josephson-junction critical currents and device inductance has been implemented. Measurements of the persistent current and of the tunneling energy between the two lowest-lying states, both in the coherent and incoherent regimes, are presented. These experimental results are shown to be in agreement with predictions of a quantum-mechanical Hamiltonian whose parameters were independently calibrated, thus justifying the identification of this device as a flux qubit. In addition, measurements of the flux and critical current noise spectral densities are presented that indicate that these devices with Nb wiring are comparable to the best Al wiring rf SQUIDs reported in the literature thus far, with a 1/f flux noise spectral density at 1 Hz of 1.3+0.7−0.5 μΦ0/Hz−−√. An explicit formula for converting the observed flux noise spectral density into a free-induction-decay time for a flux qubit biased to its optimal point and operated in the energy eigenbasis is presented
