arXiv subjects
Publications and source records attributed to Sergey Sysoev.
This paper presents an analysis of the applicability of a quantum amplitude redistribution algorithm to the data filtering problem and the results of modeling the algorithm's operation in comparison with a median filter.
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick decision (down to a single iteration) based on the correspondence between the data and the desired result, with a probability proportionate to this correspondence. Our approach allows one to calibrate the circuit to control specified proportions.
In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the best existing algorithm known to the authors. Such state preparation is essential for quantum algorithms that process large classical inputs, including matrix inversion and linear system solvers. The standard approach relies on amplitude amplification, a process that may require multiple, time-consuming oracle queries. Consequently, reducing the number of queries - and thereby the overall time complexity can lead to significant performance improvements in practice.
The new model of quantum computation is proposed, for which an effective algorithm of solving any task in NP is described. The work is based and inspired be the Grover's algorithm for solving NP-tasks with quadratic speedup compared to the classical computation model. The provided model and algorithm exhibit the exponential speedup over that described by Grover.