Tree Cluster State Generation using Percolation

Tree codes are highly coveted states for error correction against photon loss in all-photonic architectures. The linear optical (LO) method to prepare these states results in huge resource overheads as the LO Bell state measurement used to generate the states is probabilistic in nature. In this paper, we propose a percolation-based method inspired by state preparation for measurement-based quantum computation to deterministically generate infinite tree states as long as photon loss probability is up to 12% if the LO BSM success probability is 75%. This method greatly reduces the resource overhead by getting rid of the need for multiplexing. Smaller tree states used for applications such as all-photonic quantum repeater can be constructed from the large tree by performing Pauli-Z measurements on some of its qubits.