  A semiclassical simulation approach is presented for studying quantum noise
in large-scale photonic circuits incorporating an ideal Kerr nonlinearity. A
circuit solver is used to generate matrices defining a set of stochastic
differential equations, in which the resonator field variables represent random
samplings of the Wigner quasi-probability distributions. Although the
semiclassical approach involves making a large-photon-number approximation,
tests on one- and two-resonator circuits indicate satisfactory agreement
between the semiclassical and full-quantum simulation results in the parameter
regime of interest. The semiclassical model is used to simulate random errors
in a large-scale circuit that contains 88 resonators and hundreds of components
in total, and functions as a 4-bit ripple counter. The error rate as a function
of on-state photon number is examined, and it is observed that the quantum
fluctuation amplitudes do not increase as signals propagate through the
circuit, an important property for scalability.
