  Recent progress in nonlinear optical materials and microresonators has
brought quantum computing with bulk optical nonlinearities into the realm of
possibility. This platform is of great interest, not only because photonics is
an obvious choice for quantum networks, but also because it may be the only
feasible route to quantum information processing at room temperature. We
introduce a paradigm for room-temperature photonic quantum logic that
significantly simplifies the realization of various quantum circuits, and in
particular, of error correction. It uses only the strongest available bulk
nonlinearity, namely the $\chi^{(2)}$ nonlinear susceptibility. The key element
is a three-mode resonator that implements programmable bosonic quantum logic
gates. We show that just two of these elements suffice for a complete, compact
error-correction circuit on a bosonic code, without the need for measurement or
feed-forward control. An extrapolation of current progress in nonlinear optical
materials and photonic circuits indicates that such circuitry should be
achievable within the next decade.
