code: def pauli_product(*elements: Pauli) -> Pauli:
      
      result_terms = []
  
      for terms in product(*elements):
          coeff = reduce(mul, [term[1] for term in terms])
          ops = (term[0] for term in terms)
          out = []
          key = itemgetter(0)
          for qubit, qops in groupby(heapq.merge(*ops, key=key), key=key):
              res = next(qops)[1]  # Operator: X Y Z
              for op in qops:
                  pair = res + op[1]
                  res, rescoeff = PAULI_PROD[pair]
                  coeff *= rescoeff
              if res != 'I':
                  out.append((qubit, res))
  
          p = Pauli(((tuple(out), coeff),))
          result_terms.append(p)
  
      return pauli_sum(*result_terms)
docs: Return the product of elements of the Pauli algebra