Quantification of entanglement in small one-dimensional cluster states

Measurement-based quantum computation (MBQC) serves as route to universal quantum computation using just single-qubit measurements on an initial entangled resource state, typically a cluster state. MBQC is especially useful when two-qubit gates are slow and single-qubit measurements are fast and accurate. Error in gates used to create cluster states can, however, degrade entanglement. Furthermore, an efficient measure of entanglement on small cluster states would be useful for experiments as they scale up their system sizes. I will discuss a simple fidelity measure to diagnose entanglement in cluster state chains based on teleportation across the chain. Teleportation is a crucial ingredient in MBQC and thus offers a valuable probe of small cluster states. We test the fidelity measure on cluster state chains built from error-prone interactions we expect to be relevant in atomic and molecular systems, e.g., Ising and XY interactions. We establish fidelity thresholds sufficient for establishing enough entanglement to realize teleportation in these cluster states in the laboratory.