Stablaste mreže tenzora za kvantne višečestične sustave na konačnoj temperaturi

master's thesis

• Title (english): Tree tensor networks for quantum many-body systems at finite temperature
• Author: Nora Reinić
• Mentor: Simone Montangero (mentor)
• Mentor: Tamara Nikšić (mentor)
• Committee member: Tamara Nikšić (predsjednik povjerenstva)
• Committee member: Simone Montangero (član povjerenstva)
• Committee member: Mihael Srđan Grbić (član povjerenstva)
• Committee member: Nils Paar (član povjerenstva)
• Committee member: Mario Basletić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2023, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

With the second quantum revolution on its way, there is a rising interest in the development of programmable quantum devices capable of outperforming classical computers in certain tasks. Since, in reality, a physical system can never be cooled down to the absolute zero temperature, the complete description of the physics behind the quantum computing devices has to account for the finite temperature effects. However, strategies for analyzing the properties of quantum systems at finite temperature, i.e. mixed quantum states, require handling of spaces where the number of parameters scales exponentially with the system sizes, and therefore, their application is restricted to small physical systems. The class of numerical algorithms based on tensor network methods has turned out to be successful in overcoming this difficulty, extending possible simulations to large number of particles. Within this thesis, we develop and implement an efficient Tree Tensor Network based algorithm for computing the finite temperature density matrix of the many-body quantum systems. We present the numerical techniques for computing the purity, Von Neumann entropy, Rényi entropies of any order, negativity, and entanglement of formation for the mixed state systems. We apply the method on systems composed of N = 8, 16, and 32 qubits. We apply our approach to the one-dimensional quantum Ising model and successfully distinguish the three quantum phases - ferromagnetic, paramagnetic, and the disordered finite-temperature phase, as well as verify the critical point as the point of the largest entanglement. Moreover, we use our method to study the systems of neutral Rydberg atoms trapped in the optical tweezer arrays, representing a physical quantum computing and simulation platform. On these two examples of physical systems, we show that the temperature range accessible to our numerical simulations depends on the gaps between the lower energy levels of the system’s spectrum.

Abstract (croatian)

S drugom kvantnom revolucijom na putu, u posljednje vrijeme raste interes za razvojem programabilnih kvantnih uređaja sposobnih nadmašiti klasična računala u određenim zadacima. Budući da se u stvarnosti fizički sustav nikada ne može ohladiti do temperature apsolutne nule, za potpuni opis fizike kvantnih uređaja mora se uzeti u obzir efekte konačne temperature. Međutim, strategije analiziranja svojstava višečestičnih kvantnih sustava na konačnim temperaturama, tj. miješanih kvantnih stanja, zahtijevaju baratanje prostorima u kojima broj parametara raste eksponencijalno s veličinom sustava, te je njihova primjena stoga ograničena na male fizičke sustave. Klasa numeričkih algoritama temeljena na tenzorskim mrežama pokazala se uspješnom u prevladavanju ove poteškoće, proširujući dohvatljive simulacije na veći broj čestica. U okviru ovoga rada razvijen je i implementiran efikasan algoritam za izračunavanje matrice gustoće višečestičnih sustava temeljen na stablastim tenzorskim mrežama. Predstavljene su numeričke tehnike za izračunavanje čistoće stanja, Von Neumannove entropije, Rényijeve entropije proizvoljnog reda, negativnosti i prepletenosti formacije za sustave konačnih temperatura. Metoda je primijenjena na sustavima sastavljenim od N = 8, 16 i 32 qubita. Pristup je testiran na jednodimenzionalnom kvantnom Isingovom modelu gdje su uspješno detektirane tri faze - feromagnetska, paramagnetska, i neuređena faza na konačnoj temperaturi, te je kod kritične točke utvrđeno područje najveće prepletenosti. Nadalje, predložena metoda je korištena za proučavanje sustava neutralnih Rydbergovih atoma fiksiranih optičkim pincetama, koji predstavlja jednu od perspektivnih fizičkih platformi kvantnih računala. Kroz ova dva primjera, pokazano je da raspon temperature dohvatljiv našim numeričkim simulacijama ovisi o veličini energetskog procijepa u niskoenergetskom dijelu spektra sustava.

• Keywords: quantum many-body systems; entanglement; mixed states; finite temperatures; tensor networks; Rydberg atoms
• Keywords (croatian): kvantni višečestični sustavi; prepletenost; miješana stanja; konačne temperature; mreže tenzora; Rydbergovi atomi
• Language: english
• URN:NBN: urn:nbn:hr:217:027919
• Study programme: Title: Physics; specializations in: Research; Course: Research; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-05-26 08:49:27