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To my understanding, the WeightedPauliOperator class in discontinued, and should no longer be used when dealing with Pauli operators. So how should I perform arithmetic with paulis? $$ ( 3 X_1 Y_3 + 5 Z_2 X_0 ) (Z_3+2X_2X_4) = \ \text{(expanded version)} $$

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The legacy operators in Qiskit Aqua (like WeightedPauliOperator) were replaced by the operator flow function. The documentation for that replacement is here: https://github.com/Qiskit/rfcs/blob/master/0003-Aqua_0.7_operator_redesign.ipynb

However, the class is not deprecated and you are free to use it, even when it lives in the legacy module.

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