We give a modern approach to the famous Cardano and Ferrari formulas in the algebraic equations with three and four degrees. Namely, we reconstruct these formulas from the point of view of superposition principle in quantum computation based on three and four level systems which are being developed by the author.

We also present a problem on some relation between Galois theory and Qudit theory.

algebraic equations, Cardano formula, Ferrari formula, quantum computational method.