  Measurement-based quantum computing (MBQC) in linear optical systems is
promising for near-future quantum computing architecture. However, the
nondeterministic nature of entangling operations and photon losses hinder the
large-scale generation of graph states and introduce logical errors. In this
work, we propose a linear optical topological MBQC protocol employing
multiphoton qubits based on the parity encoding, which turns out to be highly
photon-loss tolerant and resource-efficient even under the effects of nonideal
entangling operations that unavoidably corrupt nearby qubits. For the realistic
error analysis, we introduce a Bayesian methodology, in conjunction with the
stabilizer formalism, to track errors caused by such detrimental effects. We
additionally suggest a graph-theoretical optimization scheme for the process of
constructing an arbitrary graph state, which greatly reduces its resource
overhead. Notably, we show that our protocol is advantageous over several other
existing approaches in terms of fault-tolerance, resource overhead, or
feasibility of basic elements.
