Correcting low-frequency noise with continuous measurement

Low-frequency noise presents a serious source of decoherence in solid-state qubits. When combined with a continuous weak measurement of the eigenstates, 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.