The Deustch-Jozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : {0, 1} → {0, 1} and suppose we have a black-box to compute f . The Deutsch-Jozsa problem is to determine if f is constant (i.e. f(x) = const, ∀x ∈ {0, 1}) or if f is balanced (i.e. f(x) = 0 for exactly half the possible input strings x ∈ {0, 1}) using as few c...

The understanding of fundamental interactions is based on the concept of quantum field theory in combination with gauge fields. It represents a unification of the theory of special relativity and quantum mechanics. Elementary particle processes are described with amazing precision. But phenomena related to gravity are not included in a satisfactory way. This would require the unification of qua...

In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantisation given by the representation theory. They form an algebra of operators which shares many properties with the...

The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to understand the classical chaos in terms of quantum mechanics. The first question has been partially solved by the Gutzwiller semiclassical trace formula for the eigen...

JPEG XR is considered as a lossy sample data compression scheme in the context of iris recognition techniques. It is shown that by optimising the JPEG XR quantisation strategy, JPEG XR default quantisation as well as JPEG2000 based iris recognition can be improved in terms of EER. The optimised JPEG XR quantisation strategy shows good performance across a wide range of iris feature extraction t...