Near-deterministic creation of universal cluster states with probabilistic Bell measurements and three-qubit resource states

We develop a scheme for generating a universal qubit cluster state using probabilistic Bell measurements without the need for feed-forward. Borrowing ideas from percolation theory, we numerically show that using unambiguous Bell measurements that succeed with 75% success probability one could build a cluster state with an underlying pyrochlore geometry such that the probability of having a spanning cluster approaches unity in the limit of infinite lattice size. The initial resources required for the generation of a universal state in our protocol are three-qubit cluster states that are within experimental reach and are a minimal resource for a Bell-measurement-based percolation proposal. Since single and multiphoton losses can be detected in Bell measurements, our protocol raises the prospect of a fully error-robust scheme.