Analysis of measurement errors for a superconducting phase qubit

We analyze several mechanisms leading to errors in a course of measurement of a superconducting fluxbiased phase qubit. Insufficiently long measurement pulse may lead to nonadiabatic transitions between qubit states 1 and 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 1 and 0 . Insufficiently fast energy relaxation after the tunneling of state 1 may cause the repopulation of the quantum well in which only the state 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 Schrödinger equation.