Single electron devices are ultra low power and extremely small devices, and suitable for implementation of large scale integrated circuits. Artificial neural networks (ANNs), which require a large number of transistors for being to be applied to practical use, is one of the possible applications of single electron devices. In order to simplify a single electron circuit configuration, we apply stochastic logic in which various complex operations can be done with basic logic gates. We design basic subcircuits of a single electron stochastic neural network, and confirm that backgate bias control and a redundant configuration are necessary for a feedback loop configuration by computer simulation based on Monte Carlo method. The proposed single electron circuit is well-suited for hardware implementation of a stochastic neural network because we can save circuit area and power consumption by using a single electron random number generator (RNG) instead of a conventional complementary metal oxide semiconductor (CMOS) RNG.