At this stage, the use of the phrase "simulation theory" is a bit of a misnomer. It is not a theory. In modern science, the term theory refers to a scientific theory; an explanation of nature that is adequately confirmed, consistent, and demonstrable in a manner that satisfies the scientific method. The lack of consistency and experimentation is the primary reason why the simulation hypothesis has not yet advanced as a theory.
That being said, there are some proponents of the simulation "theory" that refer to independent studies as evidence that lend to the label. Some of these studies include:
- The Double Slit experiment (possibly the most repeated experiment to date).
- The Delayed Choice Quantum Eraser experiment.
- The discovery of error correcting code by S. James Gates, Jr.
- The Measurement Problem.
- The Big Bang Theory and how it compares to the zero-state of a PC before it is turned on.