The form of these conditional probabilities explains the name "Gaussian" and the form of the Gaussian-binary energy function. We see that the conditional probability of x_i given \boldsymbol{h} is a normal distribution with mean b_i + \boldsymbol{w}_{i\ast}^T \boldsymbol{h} and variance \sigma_i^2 .
For the quantum mechanical calculations however, there are several ingredients which simplify our calculations.