Compensation of decoherence from telegraph noise by means of bang-bang control

摘要

With the growing efforts in isolating solid-state qubits from externaldecoherence sources, the origins of noise inherent to the material start toplay a relevant role. One representative example are charged impurities in thedevice material or substrate, which typically produce telegraph noise and canhence be modelled as bistable fluctuators. In order to demonstrate thepossibility of the active suppression of the disturbance from a {\em single}fluctuator, we theoretically implement an elementary bang-bang controlprotocol. We numerically simulate the random walk of the qubit state on theBloch sphere with and without bang-bang compensation by means of the stochasticSchr\"odinger equation and compare it with an analytical saddle point solutionof the corresponding Langevin equation in the long-time limit. We find that thedeviation with respect to the noiseless case is significantly reduced whenbang-bang pulses are applied, being scaled down approximately by the ratio ofthe bang-bang period and the typical flipping time of the bistable fluctuation.Our analysis gives not only the effect of bang-bang control on the variance ofthese deviations, but also their entire distribution. As a result, we expectthat bang-bang control works as a high-pass filter on the spectrum of noisesources. This indicates how the influence of $1/f$-noise ubiquitous to thesolid state world can be reduced.