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Insert Initialization into IR for Logical mode #650

@weinbe58

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@weinbe58

Currently the convention for Gemini logical mode is that the first non-clifford gate is state initialization. When entering the compiler pipeline we must make a distinction between the initialization gate and the other gates when rewriting gates from Squin to Native gate set. This rewrite should go as follows:

  1. Optional: Attempt to merge initialization gates non-clifford gates together into a single U3 gate.
  2. Validate the non-clifford gates are the first operations on the qubit
  3. Rewrite all non-clifford gates to U3 gates
  4. Rewrite all U3 gates to initialization statements in the logical dialect.

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