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We develop a scheme for generating a universal qubit cluster state usingprobabilistic Bell measurements without the need for feed-forward or long-timequantum memories. Borrowing ideas from percolation theory we numerically showthat using unambiguous Bell measurements that succeed with 75% successprobability, one could build a cluster state with an underlying pyrochloregeometry such that the probability of having a spanning cluster in a chosendirection approaches unity in the limit of an infinite lattice size. Theinitial resources required for the generation of a universal state in ourprotocol are 3-qubit cluster states that are within experimental reach and area minimal resource for a Bell-measurement-based percolation proposal. Sincesingle and multi-photon losses can be detected in Bell measurements, ourprotocol raises the prospect of a fully error-robust scheme.

Near-deterministic creation of universal cluster states with probabilistic Bell measurements and 3-qubit resource states