  Many proposals for solid-state photonic implementations of quantum
information processing utilize high-quality optical resonators to achieve
strong coupling between guided fields and heterogeneously incorporated qubits.
Given the practical difficulty of accurately placing quantum dots, vacancy
centers, or other such atom-like emitters throughout a complex nanophotonic
circuit, it would be natural to consider whether high-quality resonators could
be used in conjunction with bulk optical nonlinearities to create
optically-coupled qubit degrees of freedom via lithographic patterning of a
homogeneous medium. A recent limit theorem for quantum stochastic differential
equations can be used to prove rigorously that this should be possible, in
principle, using resonators incorporating a strongly Kerr-nonlinear,
$\chi^{(2)}$-nonlinear, or two-photon absorbing material with very low loss at
the fundamental optical wavelength.
