title: Reliability of quantum algorithms based on quantum Fourier transform under nonideal operation conditions
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: ÐÐ°Ð´ÐµÐ¶Ð½Ð¾ÑÑÑ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð², Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð½Ð° ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¼ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¤ÑÑÑÐµ Ð¿ÑÐ¸ Ð½ÐµÐ¸Ð´ÐµÐ°Ð»ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸ÑÑ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ
Creators: name: ÐÐ°ÑÑÐ° ÐÑÐµÐ»ÑÑÐ½Ð°, Ð¤ÑÐµÐ´Ð´Ð¸
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÐÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ñ (Ð¼Ð°Ñ.) Ð¤ÑÑÑÐµ
ÐÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°ÑÐµÐ»Ð¸
Ð²Ð¾ÑÐ¾ÑÐ° ÐÐ´Ð°Ð¼Ð°ÑÐ°
ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÐ¹ Ð¾Ð¿ÑÑ IBM
ÐºÑÐ±Ð¸Ñ
Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð¡Ð°Ð¹Ð¼Ð¾Ð½ÑÐ°
ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ñ Ð·Ð°Ð¿ÑÑÐ°Ð½Ð½Ð¾ÑÑÑ
hadamard gate
IBM quantum experience
qubit
Simons algorithm
quantum entanglement

description: Ð­ÑÐ¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¾ Ð½Ð° ÑÐ¾, ÑÑÐ¾Ð±Ñ Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°ÑÑ Ð½Ð°Ð´ÐµÐ¶Ð½Ð¾ÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð³Ð¾ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¤ÑÑÑÐµ (QFT) Ðº ÑÐ»Ð¾Ð¶Ð½ÑÐ¼ ÑÐ¸Ð³Ð½Ð°Ð»Ð°Ð¼, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÐ³Ð¾Ð´Ð½Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÑÑÑÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð±ÑÑÑÑÐ¾Ð³Ð¾ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ñ (FFT), ÑÐ¾Ð³Ð¾ ÑÐ°Ð¼Ð¾Ð³Ð¾, ÐºÐ¾ÑÐ¾ÑÐ¾Ðµ Ð»ÐµÐ¶Ð¸Ñ Ð² Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹ ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸Ð¸. Ð­ÑÐ° Ð½Ð°Ð´ÐµÐ¶Ð½Ð¾ÑÑÑ Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸ÐµÐ¼ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð¸ÑÐµÐ»ÑÐ½Ð¾ÑÑÐ¸ Ñ Ð¢Ð¤ Ð½Ð° ÑÑÐ°Ð½Ð´Ð°ÑÑÐ¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð´ÐµÐ¹ÑÑÐ²Ð¸ÑÑ Ð¸Ð· 8, 64 Ð¸ 128 ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². ÐÐ°ÑÐµÐ¼ ÐµÐ³Ð¾ Ð½Ð°Ð´ÐµÐ¶Ð½Ð¾ÑÑÑ Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÑÐµÑÑÑ Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð°ÑÐ´Ð¸Ð¾ÑÐ¸Ð³Ð½Ð°Ð»Ð°, Ð¿ÑÐ¸ ÐºÐ¾ÑÐ¾ÑÐ¾Ð¼ Ð¿Ð¾Ð»ÑÑÐ°ÐµÑÑÑ ÑÐ° Ð¶Ðµ Ð¾ÑÐ½Ð¾Ð²Ð½Ð°Ñ ÑÐ°ÑÑÐ¾ÑÐ°, ÑÑÐ¾ Ð¸ Ð¿ÑÐ¸ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ð¸ ÐÐÐ¤. ÐÐ¾ÑÐ»Ðµ ÑÐ¾Ð³Ð¾, ÐºÐ°Ðº Ð½Ð°Ð´ÐµÐ¶Ð½Ð¾ÑÑÑ Ð±ÑÐ»Ð° Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð°, Ð±ÑÐ»Ð¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ñ 2 ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð°: Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸ Ð°ÑÐ´Ð¸Ð¾ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐµÐ»ÐµÐ¿Ð¾ÑÑÐ°ÑÐ¸Ð¸ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¹ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð°ÑÐ´Ð¸Ð¾ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÑÐ±Ð¸ÑÐ¾Ð² Ð¼ÐµÐ¶Ð´Ñ Ð´Ð²ÑÐ¼Ñ ÑÐ´Ð°Ð»ÐµÐ½Ð½ÑÐ¼Ð¸ ÑÐ¾ÑÐºÐ°Ð¼Ð¸ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ð¼ ÑÐ¿Ð¾ÑÐ¾Ð±Ð¾Ð¼ Ð¸ Ð½Ð° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð¼ ÑÑÐ¾Ð²Ð½Ðµ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÐ·ÑÐº Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python Ð¸ Ð¿Ð°ÐºÐµÑ Qiskit SDK Ñ Ð¾ÑÐºÑÑÑÑÐ¼ Ð¸ÑÑÐ¾Ð´Ð½ÑÐ¼ ÐºÐ¾Ð´Ð¾Ð¼, ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½ÑÐ¹ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÑÐºÐ¾Ð¹ Ð³ÑÑÐ¿Ð¿Ð¾Ð¹ IBM. Ð¥Ð¾ÑÑ ÑÐµÐ³Ð¾Ð´Ð½Ñ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÐµ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÑ Ð½Ðµ ÑÐ²Ð»ÑÑÑÑÑ ÐºÐ¾Ð¼Ð¼ÐµÑÑÐµÑÐºÐ¸Ð¼Ð¸, Ð¾Ð½Ð¸ ÑÐ¶Ðµ ÑÑÑÐµÑÑÐ²ÑÑÑ Ð² Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½ÑÑ ÑÐµÐ½ÑÑÐ°Ñ ÐºÑÑÐ¿Ð½ÑÑ ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¸Ñ ÐºÐ¾Ð¼Ð¿Ð°Ð½Ð¸Ð¹, ÑÐ°ÐºÐ¸Ñ ÐºÐ°Ðº Google Ð¸ IBM. ÐÑÐ¾ÑÐ¼Ð°ÑÑÐ¸Ð²Ð°Ñ ÑÑÐ¾Ñ Ð´Ð¾ÐºÑÐ¼ÐµÐ½Ñ, Ð²Ñ Ð½Ð°Ð¹Ð´ÐµÑÐµ Ð¸ÑÑÐ¾Ð´Ð½ÑÐ¹ ÐºÐ¾Ð´ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð´Ð»Ñ Ð¸Ñ Ð·Ð°Ð¿ÑÑÐºÐ° Ð½Ð° ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¼ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐµ Ð¸Ð»Ð¸ Ð½Ð° ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¼ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐµ, ÑÐ°ÑÐ¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾Ð¼ Ð² Ð¾Ð±Ð»Ð°ÐºÐµ Ð¿Ð»Ð°ÑÑÐ¾ÑÐ¼Ñ IBM Quantum Experience. Ð­ÑÐ¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÐµÑ, ÑÑÐ¾, ÑÐ¾ÑÑ ÐÐ¢Ð Ð¸Ð¼ÐµÐµÑ Ð±Ð¾Ð»ÐµÐµ Ð¼ÐµÐ´Ð»ÐµÐ½Ð½ÑÐ¹ Ð¾ÑÐºÐ»Ð¸Ðº, ÑÐµÐ¼ ÐÐÐ¤, Ð¸Ð·-Ð·Ð° ÑÐ¾Ð³Ð¾, ÑÑÐ¾ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÐµ Ð¿ÑÐ¾ÑÐµÑÑÐ¾ÑÑ Ð½Ðµ Ð±ÑÑÑÑÐµÐµ, ÑÐµÐ¼ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐ½ÑÐµ Ð¿ÑÐ¾ÑÐµÑÑÐ¾ÑÑ, ÐÐ¢Ð Ð¼Ð¾Ð¶Ð½Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÑÑ ÑÐµÐ³Ð¾Ð´Ð½Ñ, Ð¸ Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÐ¼ Ð¿ÑÐ¾Ð´Ð¾Ð»Ð¶Ð¸ÑÑ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÑ Ð±Ð¾Ð»ÑÑÐµÐ³Ð¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð². ÑÐ°ÐºÐ¸Ðµ ÐºÐ°Ðº: Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ Ð¡Ð°Ð¹Ð¼Ð¾Ð½Ð°, ÐÑÐ¾Ð²ÐµÑÐ° Ð¸ Ð¨Ð¾ÑÐ°, Ñ ÑÐµÐ»ÑÑ ÑÑÐ°ÑÑ ÑÐ°ÑÑÑÑ Ð¼ÐµÐ¶Ð´ÑÐ½Ð°ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð³Ð¾Ð½ÐºÐ¸ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÑ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹.
description: This research aims to demonstrate the reliability of applying the Quantum Fourier Transform (QFT) on complex signals that are analyzed today by the Fast Transform (FFT), the same one that is the basis of current technology. This reliability is demonstrated by a performance comparison with the TF on standardized acts of 8, 64 and 128 elements. Then its reliability is demonstrated with the application of spectral analysis of an audio signal, where the same fundamental frequency is obtained that is obtained by applying the FFT. Once the reliability was demonstrated, 2 quantum algorithms were developed: an algorithm for audio signal processing and an algorithm to teleport the quantum information of the audio signal, by means of qubits between 2 distant points, in a mathematical way and at the software level using the Python programming language and the open source Qiskit SDK developed by the IBM research team. Although, today, quantum computers are not commercial, they already exist in the computing centers of large technology companies such as Google and IBM. When reviewing this document you will find the source code of the quantum algorithms to run them on a classical computer or on a quantum computer located in the cloud of the IBM Quantum Experience platform. This research shows that although the QFT of a slower response than the FFT due to the fact that quantum processors are not faster than classical computer processors, it is possible to apply the QFT today, and invites researchers to continue with the development of more quantum algorithms such as: Simon, Grover and Shor algorithms, with the aim of being part of the international quantum computing race.