An All-Photonic Quantum Repeater Scheme using Biclique Cluster State

Photon loss is the main source of error for photonic quantum repeaters. Tree codes have been used in all-photonic repeaters to correct photon loss. We study the biclique cluster state, a local-Clifford equivalent state of the tree code and known as the crazy graph in photonic quantum computing literature, as the resource state for quantum repeaters in an all-photonic architecture. A biclique is a completely symmetric bipartite graph. We encode a Bell state in the photonic biclique state such that a logical qubit of the Bell state is encoded in the physical qubits (photons) in a part of the state. Long-distance shared entanglement is generated using quantum repeaters by first sharing Bell states between neighboring repeaters and then performing Bell-state measurements (BSMs) at the repeaters. BSM on two biclique-encoded logical Bell states can be performed by performing BSM on a single pair of photons from the two logical states. If this BSM fails (due to photon loss), BSM on the next pair is attempted. Only one photon from each Bell state needs to survive for a successful logical BSM. This makes entanglement routing using the biclique-encoded logical Bell states highly loss tolerant. We analyze the entanglement generation rate vs. distance tradeoff for this repeater scheme. We have designed an algorithm for the resource-efficient generation of the biclique state by progressively fusing GHZ states using linear-optical BSM. This algorithm improves upon previous results by recycling states resulting from failed BSMs