  We introduce a simple algorithm that efficiently computes tensor products of
Pauli matrices. This is done by tailoring the calculations to this specific
case, which allows to avoid unnecessary calculations. The strength of this
strategy is benchmarked against state-of-the-art techniques, showing a
remarkable acceleration. As a side product, we provide an optimized method for
one key calculus in quantum simulations: the Pauli basis decomposition of
Hamiltonians.
