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.