Rapid-state purification protocols for a Cooper pair box

Abstract

We propose techniques for implementing two different rapid-state purification schemes, within the constraints present in a superconducting charge qubit system. Both schemes use a continuous measurement of charge $(z)$ measurements and seek to minimize the time required to purify the conditional state. Our methods are designed to make the purification process relatively insensitive to rotations about the $x$-axis, due to the Josephson tunneling Hamiltonian. The first proposed method, based on the scheme of Jacobs [Phys. Rev. A 67, 030301(R) (2003)] uses the measurement results to control bias $(z)$ pulses so as to rotate the Bloch vector onto the $x$-axis of the Bloch sphere. The second proposed method, based on the scheme of Wiseman and Ralph [New J. Phys. 8, 90 (2006)] uses a simple feedback protocol which tightly rotates the Bloch vector about an axis almost parallel with the measurement axis. We compare the performance of these and other techniques by a number of different measures.