arXiv subjects
Publications and source records attributed to Karina Zakharova.
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 search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time. Grover's algorithm gave hope to quantum computing and served as an excellent base for all possible implementations and modifications. In this paper, we propose a slightly different algorithm that increases the probability of finding the nearest value by reducing the probability of undesirable values in a controlled manner (in proportion to their difference from the desired value), as well as implementing an oracle that requires a single call without an additional ancilla qubit to redistribute the amplitudes.
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 $\sum_{i=0}^{n-1} α_i |i\rangle$, where the coefficients $α_i$ 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.