We analyze the effect of environment on the gate operation of flux-biased phase qubits. We employ the master equation for a reduced density matrix of the qubit system coupled to an Ohmic environment, described by the Caldeira-Leggett model. Numerically solving this equation, we evaluate the gate error as a function of energy splitting between qubit states, junction capacitance, and temperature. The analysis is presented for single-quadrature microwave (control) pulses as well as for two-quadrature pulses, which lower the gate error significantly for idealized systems in the absence of environment. Our results indicate that two-quadrature pulses outperform single quadrature pulses even in the presence of environment.
@article{arxiv.1008.2554,
title = {Effect of Ohmic environment on optimally controlled flux-biased phase qubit},
author = {Amrit Poudel and Maxim G. Vavilov},
journal= {arXiv preprint arXiv:1008.2554},
year = {2011}
}