Error Generator Propagation Module v2.0 Tracking

[coreyostrove]

This issue is intended to serve as a tracker for ideas and updates related to a future version 2.0 of the error generator propagation module.

• Bulk methods for probability and pauli expectation value corrections: There is currently a lot of redundant computation when computing multiple output probability or pauli expecation value corrections. E.g. instantiating a fresh stim.TableauSimulator and computing the tableau inverse to set its state is a non-trivial fraction of the overall runtime. By reworking the implementation we should be able to amortize such costs over multiple corrections reducing overhead.
• Bugfix for random error generators: Figure out a corrected construction scheme for building CP-constrained error generators w/o needing both C and A errors to appear in conjunction.
• Refactor composition code: The error generator composition code is currently ~6000 lines. There is a whole bunch of structure here which we should be able to leverage to cut this down by at least a half.
• Refactor label propagation out of the LocalStimErrorgenLabel class into a separate function in errorgenproptools.
• Refactor LocalStimErrorgenLabel into two classes. One which contains only the metadata needed for Markovian models and a child class with additional metadata relevant for non-Markovian applications. This should reduce the overhead of object instantiation (a significant portion of the overall runtime).
• More flexible iterative BCH options. There's no reason we can use mixed BCH orders across the iterative compositions, and there may be interesting performance vs. accuracy tradeoffs to explore.
• Refactor shared methods for ExplicitElementaryErrorgenBasis and CompleteElementaryErrorgenBasis into parent class.
• Generalize one-to-one correspondence between integer circuit times and error generator time indices.
• Refactor the implementation of the magnus expansion and BCH expansion to avoid the clunky loop over orders.