  In quantum information processing, knowledge of the noise in the system is
crucial for high-precision manipulation and tomography of coherent quantum
operations. Existing strategies for identifying this noise require the use of
additional quantum devices or control pulses. We present a noise-identification
method directly based on the system's non-Markovian response of an ensemble
measurement to the noise. The noise spectrum is identified by reversing the
response relationship in the frequency domain. For illustration, the method is
applied to superconducting charge qubits, but it is equally applicable to any
type of qubits. We find that the identification strategy recovers the
well-known Fermi's golden rule under the lowest-order perturbation
approximation, which corresponds to the Markovian limit when the measurement
time is much longer than the noise correlation time. Beyond such approximation,
it is possible to further improve the precision at the so-called optimal point
by incorporating the transient response data in the non-Markovian regime. This
method is verified with experimental data from coherent oscillations in a
superconducting charge qubit.
