  The characterization and mitigation of decoherence in natural and artificial
two-level systems (qubits) is fundamental to quantum information science and
its applications. Decoherence of a quantum superposition state arises from the
interaction between the constituent system and the uncontrolled degrees of
freedom in its environment. Within the standard Bloch-Redfield picture of
two-level system dynamics, qubit decoherence is characterized by two rates: a
longitudinal relaxation rate Gamma1 due to the exchange of energy with the
environment, and a transverse relaxation rate Gamma2 = Gamma1/2 + Gamma_phi
which contains the pure dephasing rate Gamma_phi. Irreversible energy
relaxation can only be mitigated by reducing the amount of environmental noise,
reducing the qubit's internal sensitivity to that noise, or through multi-qubit
encoding and error correction protocols (which already presume ultra-low error
rates). In contrast, dephasing is in principle reversible and can be refocused
dynamically through the application of coherent control pulse methods. In this
work we demonstrate how dynamical-decoupling techniques can moderate the
dephasing effects of low-frequency noise on a superconducting qubit with
energy-relaxation time T1 = 1/Gamma1 = 12 us. Using the CPMG sequence with up
to 200 pi-pulses, we demonstrate a 50-fold improvement in the transverse
relaxation time T2 over its baseline value. We observe relaxation-limited times
T2(CPMG) = 23 us = 2 T1 resulting from CPMG-mediated Gaussian pure-dephasing
times in apparent excess of 100 us. We leverage the filtering property of this
sequence in conjunction with Rabi and energy relaxation measurements to
facilitate the spectroscopy and reconstruction of the environmental noise power
spectral density.
