Alexander N. Prokopenya

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A quantum algorithm for estimating the phase, which determines the eigenvalue of a unitary operator, is discussed. It is assumed that the eigenvector of this operator and the corresponding quantum circuit are given. The memory register where the approximate phase value is stored consists of n qubits, which makes it possible to determine the phase accurate(More)
Algorithms for searching equilibrium solutions of the circular restricted four-body problem formulated on the basis of triangular Lagrange solutions of the three-body problem are discussed. For small values of one of the two system parameters, equilibrium solutions are found in the form of power series. For large values of this parameter, an algorithm for(More)
The Newtonian circular restricted four-body problem is considered. We have obtained nonlinear algebraic equations, determining equilibrium solutions in the rotating frame, and found six possible equilibrium configurations of the system. Studying the stability of equilibrium solutions, we have proved that the radial equilibrium solutions are unstable while(More)
The classical problem of three bodies with variable masses is considered in the case when the masses of all three bodies vary isotropically. Solutions to the equation of motion in terms of the osculating elements of the aperiodic quasi-conical motion and the secular perturbations of the orbital elements of the system are examined. An algorithm for(More)
We consider an application of the Mathematica package QuantumCircuit to simulation of quantum circuits implementing two of the best known quantum algorithms, namely, the Grover search algorithm and the Shor algorithm for order finding. The algorithms are discussed in detail and concrete examples of their application are demonstrated. The main features of(More)
Algorithms for searching equilibrium solutions of the circular restricted four-body problem formulated on the basis of the triangular Lagrange solutions of the three-body problem are discussed. An algorithm is proposed for calculating the bifurcation curve in the plane of system parameters that separates domains of the eight and ten equilibrium solutions.(More)
An algorithm for computing fundamental solutions to a linear system of differential equations with a periodic matrix represented by a power series in terms of a small parameter is discussed. An algorithm based on the infinite determinant method for determining boundaries between regions of stability and instability for such a system in the parameter space(More)