In this work we provide a derivation of a nonlinear sign gate (NLSG) configuration using microring resonators (mrr), and an examine of the probability of success as a function of its operational parameters. Such NLSG in a mrr extends the work of Knill-Laflamme-Milburn (KLM) version of an optical CNOT gate for quantum computing from a single point solution for the transmission coefficients using three beam splitters, to a manifold of solutions when the three beam splitters are replaced my three mrrs.

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Paul M. Alsing and E. E. Hach III, "An optical nonlinear sign shift gate using microring resonators," Proc. SPIE 10803, Quantum Information Science and Technology IV, 108030M (Presented at SPIE Security + Defence: September 11, 2018; Published: 8 October 2018); https://doi.org/10.1117/12.2325080.