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Removed the 'purity_analysis' function and its associated comments, which performed symbolic experiments to study purity and sparsity of control sets in quantum gates.
Refactor simplification functions and update gate generation functions to apply textbook simplification.
Refactor CH gate implementation to use RY gates and update parameters.
Replaced RZ gates with U1 gates for CP gate handling and adjusted parameter calculations.
Refactor quantum gate decomposition functions and simplify expressions.
Updated num_samples calculation and modified CNOT structure logic to include additional gates. Adjusted the gen_U function to use gen_P instead of gen_Rz.
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