Quantum Inf Process (2015) 14:943–950
Geometric phase gate based on the ac Stark shift
Mahmood Irtiza Hussain · Ebubechukwu O. Ilo-Okeke ·
Received: 18 October 2013 / Accepted: 22 December 2014 / Published online: 8 January 2015
© Springer Science+Business Media New York 2015
Abstract We present an alternate derivation of the geometric phase gate based on the
ac Stark shift for two qubits coupled to a shared cavity mode. Our derivation differs
from the standard one in that the qubit–light coupling occurs purely as an ac Stark
shift, rather than a state-dependent force. We derive expressions for the geometric
phases induced on the qubit states arising from the displacement of coherent light.
Simple analytic expressions are obtained for sinusodial driving of the cavity ﬁeld.
Keywords Quantum information · Entanglement generation · Quantum gates
Quantum correlations are of utmost importance and one of the indispensable ingredi-
ents of quantum information processing [1–5]. Production of fast and robust quantum
gates are one of the minimal requirements for the realization of quantum algorithms .
The inevitable interaction between system and its environment (reservoir) makes the
quantum states fragile. This feature of quantum states (systems) impairs their perfor-
M. I. Hussain (
Centre for Quantum Dynamics, Grifﬁth University, Nathan, QLD 4111, Australia
E. O. Ilo-Okeke
Department of Physics, Federal University of Technology, P. M. B. 1526, Owerri, Imo State, Nigeria
E. O. Ilo-Okeke · T. Byrnes
National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-Ku, Tokyo 101-8430, Japan
New York University, 1555 Century Ave, Pudong, Shanghai 200122, China