What is complexity, and how should it be studied mathematically? In the interpretation that we adopt, there are several underlying common themes to complexity theories. The basic ground rules are these: There is a family F of some mathematical objects under consideration. The elements of some subset S ⊆F are deemed simple. Also, there are certain composition rules that allow one to put together...

In this paper we present some measures of complexity of decomposable structures. The literature on complexity is reviewed and then the distinction among different measures of complexity is discussed. At first, a broad definition of complex systems is provided and the main characteristics of such systems are described briefly. In particular, a complex system is defined as a network of many highl...

A bstract We study the conditions under which, given a generic quantum system, complexity metrics provide actual lower bounds to circuit associated set of gates. Inhomogeneous cost functions — many examples which have been recently proposed in literature are ruled out by our analysis. Such measures shown be unrelated general and produce severe violations Lloyd’s bound simple situations. Among d...