Low-frequency noise presents a serious source of decoherence in solid-state
qubits. When combined with a continuous weak measurement of the eigenstates,
the low-frequency noise induces a second-order relaxation between the qubit
states. Here we show that the relaxation provides a unique approach to
calibrate the low-frequency noise in the time-domain. By encoding one qubit
with two physical qubits that are alternatively calibrated, quantum logic gates
with high fidelity can be performed.Comment: 10 pages, 3 figures, submitte