Geometric phase gate with a quantized driving field

Abstract

ABSTRACT We have studied the performance of a geometric phase gate with a quantized driving “eld numerically, anddeveloped an analytical approximation that yields some preliminary insight on the way the qubit becomesentangled with the driving “eld.Keywords: Quantum computation, adiabatic quantum gates, geometric quantum gates 1. INTRODUCTION It was “rst suggested by Zanardi and Rasetti, 1 that the Berry phase (non-abelian holonomy) 2–4 might in principleprovide a novel way for implementing universal quantum computation. They showed that by encoding quantuminformation in one of the eigenspaces of a degenerate Hamiltonian H one can in principle achieve the fullquantum computational power by using holonomies only. It was then thought that since Berrys phase is apurely geometrical eect, it is resilient to certain errors and may provide a possibility for performing intrinsicallyfault-tolerant quantum gate operations. In a paper by Ekert et.al, 5 a detailed theory behind the implementationof geometric computation was developed and an implementation of a conditional phase gate in NMR was shownby Jones et.al.