Azad, Fariha;
(2024)
Tensor networks for classical and quantum simulation of open and closed quantum systems.
Doctoral thesis (Ph.D), UCL (University College London).
Preview |
Text
Thesis_2.pdf - Accepted Version Download (5MB) | Preview |
Abstract
Tensor networks are an invaluable tool for the study of quantum systems. In this thesis we use tensor networks, and more directly matrix product states, to simulate both open and closed quantum systems. In the first part we study the one-dimensional spin-1/2 J1-J2 model using a path integral constructed over matrix product states. This is a spin-model with neigh- bour (of strength J1) and next-nearest neighbour (J2) interactions. We show how this treatment is able to capture the transition from antiferromagnetic order to singlet order at the semi-classical, saddle point level, since saddle points support non-trivial entanglement structure. Taking an appropriate continuum limit, that is a generalisation of the Haldane map, we recover the previously known field theory with the crucial topological terms that determine the nature of the phase transition. In the second part we introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling to the environment. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. Finally, we present a time-evolution algorithm for ion-trap based quantum com- puters. Here we optimise translationally invariant quantum circuit representations of states to simulate the dynamical phase transition of the quantum transverse-field spin-1/2 Ising model. We implement efficient sequential quantum circuits that are inspired by infinite matrix product states. Preliminary results on ion-trap emulators show promise for the utility of this approach.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Tensor networks for classical and quantum simulation of open and closed quantum systems |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2024. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10187404 |
Archive Staff Only
 |
View Item |
