Bernstein polynomial

A similar curve description was achieved by Philip De Casteljeau at the French firm Citroen. Nevertheless, the method of approximation of the control polygon was linked to the name of Bezier in the literature even if the description of the curves uses functions other than Bernstein polynomials. 

It is noteworthy that the statistical error of F(x) depends at any point x on the statistical errors of all control points, weighed by the square of the Bernstein polynomial associated with the respective position in x space. 

Where P represent the n+1 vertices of a characteristic polygon and Bi,n(u) is the Bernstein polynomial blending function ... 

Of interest to us is that quantum computers add a completely new class to this hierarchy the class of non-deterministic algorithms that can be solved in polynomial time on a quantum computer, so-called BQP [Bernstein 1997], The key to these fantastic quantum algorithms, or so everybody believed until recently, was the presence of in these systems. 

Only recently Bernstein and Vazirani [6] proved the existence of a quantum Turing machine whose simulation overhead is polynomial bounded. This is what computer scientists call an efficient simulation. The result is of crucial importance for quantum complexity theory Only machines that can efficiently simulate any other Turing machine are called universal. To be called universal, it is not sufficient that the machine is simply able to simulate other Turing machines. 

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