Single-shot charge qubit read-out using a single electron transistor: back-action and fidelity

Abstract

We analyze the fidelity of single shot read-out of a superconducting charge qubit (Cooper pair box) using a capacitively coupled radio-frequency single electron transistor (RF-SET). By comparing the time needed to separate the two qubit states with the time after which the initial state of the qubit is destroyed, due to back-action from the SET, we find that a signal to noise ratio substantially larger than unity is obtainable. To evaluate the back-action at the relevant frequencies, which are comparable to the tunneling rates in the SET, we use a fully quantum mechanical expression for the voltage fluctuations on the SET island.