Optical cluster-state generation with unitary averaging

Cluster states are the essential resource used in the implementation of fusion-based quantum computation (FBQC). We introduce a method to generate high-fidelity optical cluster states by utilizing the concept of unitary averaging. This error-averaging technique is entirely passive and can be readily incorporated into the proposed PsiQuantum FBQC architecture. Using postselection and the redundant encoding of fusion gates, we observe an enhancement in the average fidelity of the output cluster state. As a generalization, we also show an improvement in the linear optical Bell-state measurement (BSM) success probability when the BSM is imperfect.