Background: Recently, there has been a flurry of attention focused on the benefits of synthetic control patients in clinical trials. The ability to reduce the burden on control subjects with subjects in clinical trials for complex diseases like Alzheimer's Disease would drastically improve the search for beneficial therapies. Objective: To demonstrate a machine learning model is capable of simulating Alzheimer's Disease progression and generate digital control subjects that are statistically indistinguishable from actual controls. Methods: We developed a machine learning model of Alzheimer's Disease progression trained with data from 4897 subjects from 28 clinical trial control arms involving early or moderate Alzheimer's Disease. The model is an example of a Conditional Restricted Boltzmann Machine (CRBM), a kind of undirected neural network whose properties are well suited to the task of modeling clinical data progression. The model generates values for 47 variables for each digital control subject at three-month intervals. Results: Based on a statistical analysis comparing data from actual and digital control subjects, the model generates accurate subject-level distributions across variables and through time that are statistically indistinguishable from actual data. Conclusion: Our work demonstrates the potential for the CRBMs to generate digital control subjects that are statistically indistinguishable from actual control subjects, with promising applications for Alzheimer's Disease clinical trials.