The visibility study of S-T$_+$ Landau-Zener-St\"uckelberg oscillations   without applied initialization
  Probabilities deduced from quantum information studies are usually based on averaging many identical experiments separated by an initialization step. Such initialization steps become experimentally more challenging to implement as the complexity of quantum circuits increases. To better understand the consequences of imperfect initialization on the deduced probabilities, we study the effect of not initializing the system between measurements. For this we utilize Landau-Zener-St\"uckelberg oscillations in a double quantum dot circuit. Experimental results are successfully compared to theoretical simulations. 
G. Granger, G. C. Aers, S. A. Studenikin, A. Kam, P. Zawadzki, Z. R.   Wasilewski, and A. S. Sachrajda
cond-mat.mes-hall