Formulas and algorithms for quantum differentiation of quantum Bernstein bases and quantum Bézier curves based on quantum blossoming

► We introduce the homogeneous variants of the quantum blossoms. ► We derive relationships between the homogeneous quantum blossoms and the quantum derivatives. ► We present explicit formulas for the quantum derivatives of the quantum Bern stein bases. ► We generate recursive algorithms for the quantum derivatives of quantum Bézier curves.