An optical nonlinear sign shift gate using microring resonators

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.