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In quantum computation, quantum coherence must be maintained during gateoperation. However, in physical implementations, various couplings with theenvironment are unavoidable and can lead to a dephasing of a quantumbit(qubit). The background charge fluctuations are an important dephasingprocess, especially in a charge qubit system. We examined the dephasing rate ofa qubit due to random telegraph noise. Solving stochastic differentialequations, we obtained the dephasing rate of a qubit constructed of acoupled-dot system; we applied our results to the charge Josephson qubitsystem. We examined the dephasing rates due to two types of couplings betweenthe coupled-dot system and the background charge, namely, fluctuation in thetunnel coupling constant and fluctuation in the asymmetric bias. For a strongcoupling condition, the dephasing rate was inversely proportional to the timeconstant of the telegraph noise. When there is fluctuation in the tunnelcoupling constant, Gaussian decay occurs in the initial regime. We alsoexamined the rate of dephasing due to many impurity sites. For a weak couplingcondition with fluctuation in the asymmetric bias, the obtained dephasing ratecoincided with that obtained by the perturbation method using the spectralweight of a boson thermal bath, which is proportional to the inverse of thefrequency.Comment: 10 pages, 6 figures, RevTeX, to be published in Phys. Rev.

Dephasing due to background charge fluctuations