Tool for checking basic fault tolerance

Sometimes user sees logical error rate always higher than physical error rate but not sure why this is happening. It's often a question about whether this is a decoder problem or encoder problem (how the fault-tolerant circuit is designed). Generally, user would also like to check if a constant number of combination of the physical errors would cause a logical error. None of these functionalities are easy to build from user's perspective because the simulation happens inside deq-runtime. However, if we could provide such a functionality pointing to which gadget's which error (line number), and show the syndrome information, and show which set of errors that the decoder infers, this would be pretty helpful for users.

Start by investigating how the simulation runs inside deq-runtime and how fault-tolerant circuits expose gadgets and errors. The finished tool should identify the gadget and error line causing a logical error, show syndrome information, and report which physical-error sets the decoder infers.