Parity-encoding-based quantum computing with Bayesian error tracking

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 the fault-tolerance and resource overhead.