Scheme for Efficient Construction of 2-Dimensional Qutrit Cluster State

Utilizing quantum entangling gates with an arbitrary small success probability p, we propose a three-step scheme for conclusively constructing 2-dimensional (2D) lattice qutrit cluster states (QTCS). We first prepare one-dimensional (1D) QTCS, then use the 1D states to generate cross-shaped QTCS, and finally take the cross-shaped QTCS as "building blocks" to construct 2D lattice QTCS. In our scheme parallel operations are executed so that the construction process is significantly accelerated. Our scheme provides a potential efficient way to implement realistic one-way quantum computers.