Izvođenje Shorovog algoritma za faktorizaciju cijelih brojeva na kvantnim računalima iz porodice IBM Q Experience

master's thesis

• Title (english): Execution of Shor's factoring algorithm on IBM Q Experience quantum computers
• Author: Marko Blažević
• Mentor: Saša Ilijić (mentor)
• Mentor: Marinko Jablan (komentor)
• Committee member: Marinko Jablan (predsjednik povjerenstva)
• Committee member: Saša Ilijić (član povjerenstva)
• Committee member: Željko Skoko (član povjerenstva)
• Committee member: Danko Radić (član povjerenstva)
• Committee member: Maja Planinić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-03-04, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Američka tvrtka IBM omogućila je 2016. godine da kvantna računala budu javno dostupna. Koristeći grafičko korisničko sučelje IBM Quantum Composer moguće je implementirati jednostavne kvantne algoritme. Slavni Shorov algoritam iz 1994. godine za faktorizaciju cijelih brojeva najbolje pokazuje moć kvantnih računala. U ovom radu opisane su osnove kvantne informacije i algoritama. Dana su svojstva i detaljno su opisana kvantna vrata koja se najčešće koriste pri kreiranju kvantnih krugova. Diplomski rad analizira matematičku razradu djelovanja kvantnog Fourierovog transformata na sustav n kvantnih bitova. Također, dat je kvantni krug koji implementira kvantnu Fourierovu transformaciju. Prikazna je procedura faktorizacije brojeva 15, 21, i 35 Shorovim algoritmom. Koristeći IBM Quantum Composer implementirani su kvantni krugovi za kvantnu Fourierovu transformaciju kao i Shorov algoritam za faktorizaciju broja 15.

Abstract (english)

In the year of 2016 American company IBM made quantum computers publicly available. Using the graphical user interface IBM Quantum Composer it is possible to implement various quantum algorithms. The famous Shor’s algorithm from the year of 1994 used for the integer factorisation is the foremost way of showing how powerful quantum computers are. In this work, the basics of quantum information and algorithms are described. The properties, as well as a brief description of the quantum gates most frequently used in creating quantum circuits are given. The thesis analyses the mathematical examination of applying quantum Fourier transform on a system of quantum bits. Also, a quantum circuit which implements quantum Fourier transform is given. The procedure of factoring the numbers 15,21, and 31 using Shor’s algorithm is presented. Quantum circuits for the quantum Fourier transform, as well as Shor’s algorithm for factoring the number 15, were implemented using IBM quantum composer.

• Keywords: Kvantni bit; Shorov algoritam; kvantna vrata; kvantni Fourierov transformat; IBM Quantum Composer
• Keywords (english): quantum bit; Shor’s algorithm; quantum gate; IBM Quantum Composer; quantum Fourier transform
• Language: croatian
• URN:NBN: urn:nbn:hr:217:066959
• Study programme: Title: Physics; specializations in: Education; Course: Education; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra edukacije fizike (magistar/magistra edukacije fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-03-18 15:56:41