title: Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐºÐ° Ð½Ð° ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¼ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Quantum gradient descent implementation
Creators: name: Ð¢Ð°ÑÐ¸ÑÐ¾Ð², ÐÐ±ÑÐ»Ñ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: 2023
Subjects: ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑ
ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÐµ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ
Ð¼ÐµÑÐ¾Ð´ Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐºÐ°
Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð°Ñ ÑÐµÑÑ
computer
quantum computing
gradient descent algorithm
neural network

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ, ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ñ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð¸ÑÐµÐ»ÑÐ½Ð¾ÑÑÐ¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐºÐ° Ð½Ð° ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¼ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐµ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1) Ð°Ð½Ð°Ð»Ð¸Ð· Ð¸ Ð²ÑÐ±Ð¾Ñ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð³Ð¾ ÑÑÑÑÐ¾Ð¹ÑÑÐ²Ð°; 2) ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐºÐ° Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÑ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹; 3) ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¸ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð²; 4) ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¹ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÑÐ¸; 5) ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¸ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¹ ÑÐµÑÐµÐ¹. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ°Ð±Ð¾ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÐ¹ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑ, Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÑ ÐµÐ³Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð±ÑÑÑÑÐ¾Ð³Ð¾ Ð¸ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼ÐµÑÐ¾Ð´Ð° Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐºÐ°. Ð¢Ð°ÐºÐ¶Ðµ Ð² ÐºÐ°ÑÐµÑÑÐ²Ðµ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ° Ð±ÑÐ»Ð° ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð° Ð¸ Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð°Ñ ÑÐµÑÑ Ð¿Ð¾ ÑÐ°ÑÐ¿Ð¾Ð·Ð½Ð°Ð²Ð°Ð½Ð¸Ñ ÑÑÐºÐ¾Ð¿Ð¸ÑÐ½ÑÑ ÑÐ¸ÑÑ Ð½Ð° Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ð¸. Ð ÐµÐ·ÑÐ»ÑÑÐ°Ñ ÑÐ°Ð±Ð¾ÑÑ Ð¼Ð¾Ð¶Ð½Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ Ñ ÑÐµÐ»ÑÑ Ð¾Ð·Ð½Ð°ÐºÐ¾Ð¼Ð»ÐµÐ½Ð¸Ñ Ñ ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸ÐµÐ¹ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÑ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹, Ð° ÑÐ°ÐºÐ¶Ðµ Ð´Ð»Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¸Ñ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð½Ð° Ð´Ð°Ð½Ð½Ð¾Ð¼ ÑÑÐ°Ð¿Ðµ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ñ.
description: This work is devoted to the research, implementation and analysis of the performance of the gradient descent algorithm on a quantum computer. The research set the following goals: 1) analysis and selection of a quantum device; 2) implementation of the gradient descent algorithm using quantum computing; 3) comparison of classical and quantum algorithms; 4) implementation of a quantum neural network; 5) comparison of classical and quantum networks. As a result of the work, a quantum computer and the possibility of its application for fast and efficient problem solving using the gradient descent method are investigated. Also, as an experiment, a quantum neural network for recognizing handwritten digits in an image was implemented and demonstrated. The result of the work can be used to familiarize with the technology of quantum computing, as well as to analyze their effectiveness at this stage of development.