Quantum Hashing for Finite Abelian Groups

We propose a generalization of the quantum hashing technique based on the notion of the small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for succinct quantum presentation of elements of any finite abelian group, which can be used in various computational and cryptographic scenarios. The known quantum fingerprinting schemas turn out to be the special cases of the proposed quantum hashing for the corresponding abelian group

Quantum Communications Based on Quantum Hashing

In this paper we consider an application of the recently proposed quantum hashing technique for computing Boolean functions in the quantum communication model. The combination of binary functions on non-binary quantum hash function is done via polynomial presentation, which we have called a characteristic of a Boolean function. Based on the characteristic polynomial presentation of Boolean functions and quantum hashing technique we present a method for computing Boolean functions in the quantum one-way communication model, where one of the parties performs his computations and sends a message to the other party, who must output the result after his part of computations. Some of the results are also true in a more restricted Simultaneous Message Passing model with no shared resources, in which communicating parties can interact only via the referee. We give several examples of Boolean functions whose polynomial presentations have specific properties allowing for construction of quantum communication protocols that are provably exponentially better than classical ones in the simultaneous message passing setting

Algorithms for Quantum Branching Programs Based on Fingerprinting

In the paper we develop a method for constructing quantum algorithms for computing Boolean functions by quantum ordered read-once branching programs (quantum OBDDs). Our method is based on fingerprinting technique and representation of Boolean functions by their characteristic polynomials. We use circuit notation for branching programs for desired algorithms presentation. For several known functions our approach provides optimal QOBDDs. Namely we consider such functions as Equality, Palindrome, and Permutation Matrix Test. We also propose a generalization of our method and apply it to the Boolean variant of the Hidden Subgroup Problem

Towards a Unified Theory of Massless Superfields of All Superspins

We describe the ``universal'' action for massless superfields of all superspins in N = 1, D = 4 anti-de Sitter superspace as a gauge theory of unconstrained superfields taking their values in the commutative algebra of analytic functions over a one-sheeted hyperboloid in $R^{3,1}$. The action is invariant under N = 2 supersymmetry transformations which form a closed algebra off the mass-shell.Comment: 12 pages, LaTe

Mathematical Approaches in Studying the Ideal Image of the Goal

The article outlines the possible approaches in the mathematical computations of integrated behavioral units in functional systems supporting homeostasis through in behavioral changes. By an imbalance in the homeostasis system which initiates adaptive behavior we assume: for metabolism – a departure of the parameters from the “normal zone” to the level of a suprathreshold sensitivity of the receptors; for structures of the psychological and social spectra – to the “cognized-not cognized”, “acceptable-not acceptable” levels. For the system analysis of goal-directed behavior dynamics, we present a combination of the “creation – retention” of the ideal image of the goal and the entire effector structure of the integrated behavioral unit by introducing an integrating term, motivational gradient. The integrated Behavioral Unit (BU) is described as a psychophysiological metamer in behavioral continuum, including a mathematical description of the BU as a whole including its elements viz., the ideal image of the goal and the motivational gradient. The hemodynamic equivalent of the motivational gradient (the scalar gradient) and subjective time (the time marker) are used as the BU markers. For the mathematical description, we use the mathematical apparatus of topological spaces and elements of the string theory to open up opportunities for new approaches in psychology and neurobiology

Fast and robust two- and three-qubit swapping gates on multi-atomic ensembles in quantum electrodynamic cavity

Creation of quantum computer is outstanding fundamental and practical problem. The quantum computer could be used for execution of very complicated tasks which are not solvable with the classical computers. The first prototype of solid state quantum computer was created in 2009 with superconducting qubits. However, it suffers from the decoherent processes and it is desirable to find more practical encoding of qubits with long-lived coherence. It could be single impurity or vacancy centers in solids, but their interaction with electromagnetic radiation is rather weak. So, here, ensembles of atoms were proposed for the qubit encoding by using the dipole blockade mechanism in order to turn multilevel systems in two level ones. But dipole-dipole based blockade introduces an additional decoherence that limits its practical significance. Recently, the collective blockade mechanism has been proposed for the system of three-level atoms by using the different frequency shifts for the Raman transitions between the collective atomic states characterized by a different number of the excited atoms. Here, we propose two qubit gate by using another collective blockade mechanism in the system of two level atoms based on exchange interaction via the virtual photons between the multi-atomic ensembles in the resonator. Also we demonstrate the possibility of three qubit gate (Controlled SWAP gate) using a suppression of the swap-process between two multi-atomic ensembles due to dynamical shift of the atomic levels controlled by the states of photon encoded qubit

Specific features of space-time variations of ozone during the development of intensive tropical disturbances

An analysis of specific features of space-time variations of ozone in the tropical areas which has been performed on the basis of processing of the results of special expedition studies in the Atlantic and Pacific in 1987-1990 and the data of observations at the stations of the world ozonometric network over the 25-year period. The existence of a cause-and-effect relation has been revealed between the processes determining tropical cyclone (TC) development, and specific features of variations of the total content of ozone (TCO) and the vertical distribution of ozone (VDO) in the regions of TC action. Characteristic features of day-to-day and daily variations of TCO during TC development have been found. On the periphery of a developing TC, 1-4 days before it reaches the stage of storm, TCO increases, on average, by 5-8 percent, and a substantial increase in the concentration of ozone occurs in the middle and upper troposphere. The most probable physical mechanisms relating the observed specific features of ozone variations to TC evolution have been suggested. A hypothesis of the possibility of using ozone as an indicator for early prediction of TC development has been substantiated