Geometric methods for construction of quantum gates

Shingo Kukita, Yasushi Kondo

Klaus Mølmer, Anders Søndberg Sørensen, Xiaoguang Wang

Yu-Mei Gao, Xin-Ding Zhang, Lian Hu

We present a novel evolution method to obtain pure geometric phase with orthogonal superposed initial state method (OGSM). As examples we illustrate in detail the geometric evolution both in NMR and superconducting Josephson junction systems, which may be further designed to construct fault-tolerant geometric quantum gates. In the end we also propose a simple way to construct topological quantum gates based on OGSM.

Yibin He, Li Wang

Zakaria Giunashvili

The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. These methods are shown to be very useful for the problem of constructing an universal set of gates for quantum computations: the well-known result that the set of all one-bit gates together with almost any one two-bit gate is universal is considered from the control theory viewpoint.

Shi-fan Qi, Jun Jing

We propose a novel method for constructing geometric quantum gates using three- or two-level systems, in which a controllable variable, the detuning between the driving frequency and the atomic energy spacing, is introduced to realize geometric transformations. In particular, we have two instantaneous eigenstates with opposite eigenvalues constituting a closed loop in the parameter space. The accumulated dynamical phase is then exactly cancelled when the loop is completed, which is beyond the traditional parallel-transport restriction. We apply the transitionless quantum driving method to enhance the speed and fidelity of geometric gates. Gate fidelity in the presence of decoherence is also estimated.