Add ability to expose a change of measurement basis in tsim

[jasonhan3]

Given a circuit, having the ability to compile it once and changing the measurement basis for the same circuit would be useful, so that when running a circuit in a different measurement basis, you would not need to recompile the circuit

[zsxqblz]

for context this will be helpful for simulating Pauli shadow. It might able to be useful to have the ability to change the angle of the magic gates, which should only change the coefficients in the low-stabilizer-rank decomposition.

[rafaelha]

Unfortunately, changing the measurement basis (e.g. from Z to X) conflicts with Tsim's compilation. This is because Tsim can compile a circuit once for all noise configuration (i.e. a compiled circuit can be sampled efficiently for arbitrarily inserted Pauli gates). But changing a Z basis to X would imply a H gates, which is not a Pauli gate.

Compiling one circuit for different magic angles is also difficult. This is because in stabilizer rank decomposition, multiple rotations of the same angle are decomposed together. If one of these angles was changed after the fact, this would invalidate the decomposition. One place where this could work, however, is for circuits where all rotation angles are the same.

One alternative approach is to introduce a better version of the cutting decomposition that builds a parameterized diagram. Instead of building a tensor of exponential size, the compilation routine would build a polynomial-size tensor with free parameters. This significantly cuts the compilation time. I did some experiments with this and I'm happy to chat and build a full implementation.