Abstract:
A method for generating a random number sequence whose randomness properties are determined a priori, includes defining a parametric map, calculating, in function of parameters of the map, the entropy and the Lyapunov exponent of random number sequences obtainable using the parametric map, and identifying at least a set of values of parameters for which the entropy and the Lyapunov exponent are positive numbers the map has no attracting point. The method further includes assigning a pre-established value as a first feedback value and cyclically carrying out the following steps for generating a random number sequence: determining the parameters inside the set as the numerical values of respective physical quantities, outputting a random number, according to the map with the parameters and the assigned feedback value, and assigning as new feedback value the output random number.
Abstract:
A hardware quantum gate for running quantum algorithms in a very fast manner exploits the fact that a large number of multiplications required by an entanglement operation of the quantum algorithm provides a null result since only one component per row of the entanglement matrix UF is not a null. The entanglement operation generates an entanglement vector by permuting pairs of opposite components of a linear superposition vector, depending on the value assumed by the function f. More specifically, if function f is null in correspondence to the vector identified by the first (leftmost) n qubits in common with the two nnull1 qubit vectors, in which a pair of opposite components of the superposition vector is referred to, then the corresponding pair of components of the entanglement vector is equal to that of the superposition vector, otherwise it is the opposite.
Abstract:
A quantum gate performs the superposition operation of a Grover's or of a Deutsch-Jozsa's quantum algorithm in a very fast manner. This is done by performing all multiplications by using logic gates that immediately outputs the result. The superposition operation includes performing the Hadamard rotation over an input set of vectors for producing a set of rotated vectors, and calculating the tensor product of all the rotated vectors for outputting a linear superposition set of vectors. The tensor product of all the rotated vectors is carried out by the logic gates.
Abstract:
A quantum gate for running a Grover's quantum algorithm using a binary function having a vector basis of n qubits is provided. The quantum gate includes a superposition subsystem, an entanglement subsystem and an interference subsystem. The interference subsystem performs an interference operation on components of entanglement vectors for generating components of output vectors. The interference subsystem performs the interference operation in a very fast manner by using an adder receiving as input signals representing even or odd components of an entanglement vector, and generating a sum signal representing a weighted sum with a scale factor of the even or odd components. The interference subsystem also includes an array of adders each input with a respective signal representative of an even or odd component of an entanglement vector and with the weighted sum signal, and generates a signal representative of an even or odd component of an output vector as a difference between the weighted sum signal and the signal representing an even or odd component of an entanglement vector.
Abstract:
A circuit implementing a non-integer order dynamic system includes a neural network that receives at least one input signal and generates therefrom at least one output signal. The input and output signals are related to each by a non-integer order integro-differential relationship through the coefficients of the neural network. A plurality of such circuits, implementing respective non-integer order controllers can be interconnected in an arrangement wherein any of the integral or differential blocks included in one of these circuits generates a signal which is fed to any of the integral or differential blocks of another circuit in the system.