Loss-tolerant teleportation on large stabilizer states

We present a general method for finding loss-tolerant teleportation on large, entangled stabilizer states using only single-qubit measurements, known as "stabilizer pathfinding" (SPF). For heralded loss, SPF is shown to generate optimally loss-tolerant measurement patterns on any given stabilizer state. Furthermore, SPF also provides highly loss-tolerant teleportation strategies when qubit loss is unheralded. We provide a fast algorithm for SPF that updates continuously as a state is generated and measured, and which is therefore suitable for real-time implementation on a quantum-computing device. When compared to previous heuristics for loss-tolerant teleportation on graph states, SPF provides considerable gains in tolerance to both heralded and unheralded loss, achieving a near-perfect teleportation rate ($> 95\%$) in the regime of low qubit loss ($< 10\%$) on various graph state lattices. Using these results we also present evidence which points towards the existence of loss-tolerant thresholds on such states, which in turn indicates that the loss-tolerant behaviour we have found also applies as the number of qubits tends to infinity. Our results represent a significant advance towards the realistic implementation of teleportation in both large-scale and near-future quantum architectures that are susceptible to qubit loss, such as linear optical quantum computation and quantum communication networks.