Generating and verifying graph states for fault-tolerant topological measurement-based quantum computing in two-dimensional optical lattices

We propose two schemes for implementing graph states useful for fault-tolerant topological measurement-based quantum computation in two-dimensional (2D) optical lattices. We show that bilayer cluster and surface-code states can be created by global single-row and controlled-Z operations. The schemes benefit from the accessibility of atom addressing on 2D optical lattices and the existence of an efficient verification protocol which allows us to ensure the experimental feasibility of measuring the fidelity of the system against the ideal graph state. The simulation results show potential for a physical realization toward fault-tolerant measurement-based quantum computation against dephasing and unitary phase errors in optical lattices.