Cluster states from Heisenberg interactions

We show that a special type of entangled states, cluster states, can be created with Heisenberg interactions and local rotations in $2d$ steps where $d$ is the dimension of the lattice. We find that, by tuning the coupling strengths, anisotropic exchange interactions can also be employed to create cluster states. Finally, we propose electron spins in quantum dots as a possible realization of a one-way quantum computer based on cluster states.

Figure 1

(a) A one-dimensional cluster (a qubit chain). The connecting lines represent the interaction between nearest neighbors. (b) An alternative way to entangle a one-dimensional cluster. The qubits which are connected by straight lines are entangled in the first step and those connected by semicircles are entangled in the subsequent step.