Analysis of measurement errors for a superconducting phase qubit
Qin Zhang, Abraham G. Kofman, John M. Martinis, Alexander N. Korotkov · Physical Review B · 2006
We analyze several mechanisms leading to errors in a course of measurement of a superconducting flux-biased phase qubit. Insufficiently long measurement pulse may lead to nonadiabatic transitions between qubit states \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩, before tunneling through a reduced barrier is supposed to distinguish the qubit states. Finite (though large) ratio of tunneling rates for these states leads to incomplete discrimination between \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩. Insufficiently fast energy relaxation after the tunneling of state \ensuremath{\mid}1⟩ may cause the repopulation of the quantum well in which only the state \ensuremath{\mid}0⟩ is supposed to remain. We analyze these types of measurement errors using analytical approaches as well as a numerical solution of the time-dependent Schr\"odinger equation.