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master's thesis
Kvantni algoritmi
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:536760
Delić, Karlo
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Delić, K. (2024). Kvantni algoritmi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:536760

Delić, Karlo. "Kvantni algoritmi." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:536760

Delić, Karlo. "Kvantni algoritmi." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:536760

Delić, K. (2024). 'Kvantni algoritmi', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:536760

Delić K. Kvantni algoritmi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:536760

K. Delić, "Kvantni algoritmi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:536760

Metadata
TitleKvantni algoritmi
Title (english)Quantum algorithms
AuthorKarlo Delić
MentorMatija Kazalicki (mentor)
Committee memberMatija Kazalicki (predsjednik povjerenstva)
Committee memberZvonimir Bujanović (član povjerenstva)
Committee memberRobert Manger (član povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-02-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu istražujemo algoritamske pristupe primjenjive na kvantne sustave, posebno Fermi-Hubbardov model. Uz povijesni osvrt i motivaciju, dan je i kratki pregled potrebnih fizikalnih i računalnih koncepata. Nakon što je model predstavljen i neki od njegovih rubnih slučajeva analitički riješeni, pokazujemo kako koristiti klasične i kvantne simetrije da bismo njegov Hamiltonijan reducirali na lako rješive blokove. Intuicija i razumijevanje izgrađeni u ovom dijelu omogućavaju nam da postupno izgradimo ansatz za kvantni varijacijski algoritam. Nakon konstrukcije sklopa, provodimo simulacije koje otkrivaju da predloženo rješenje radi precizno s različitim optimizatorima, izvršava se u kratkom vremenu te je robusno na uvođenje šuma koji potječe od konačnog broja mjerenja. Konačno, ističemo nekoliko prirodnih smjerova za buduća istraživanja.
Abstract (english)
In this work, we explore algorithmic approaches applicable to quantum systems, specifically the Fermi-Hubbard model. After outlining the motivation to do so, we follow with a brief overview of necessary physical and computing concepts. Once the model is introduced and some of its limiting cases are solved analytically, we demonstrate how to use classical and quantum symmetries to reduce its Hamiltonian into easily solvable blocks. The intuition and understanding built doing so allow us to gradually build the quantum ansatz for the Variational Quantum Eigensolver. After constructing the circuit, we conduct simulations, revealing that the proposed solution works precisely with various optimizers and runs in a short time, all while being robust even when the shot noise is introduced. Finally, we outline some natural directions for future research.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:536760
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar računarstva i matematike (sveučilišni magistar računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-03-13 08:43:00