Nico-Katz, Alexander A.;
(2023)
Informational Aspects of Quantum Many-Body Systems.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
The prevailing theme of modern quantum many-body physics is circumscribed by the question: are such systems useful? Can we use them to simulate something, or compute the answer to a problem? Despite this, information-theoretic analyses of quantum many-body systems are rare. This thesis seeks to address that by investigating informational aspects of problems that might be conventionally delegated to the condensed matter community. I start by investigating ‘local memory’ in systems that exhibit some form of ergodicity-breaking. A quantitative investigation of how much information is actually retained, and whether or not that information can be accessed, is lacking in this context. I introduce an information-theoretic framework and a criteria by which ‘local memory’ can be quantitatively defined. I analyze many-body localized (MBL) and quantum scarred systems; both touted to exhibit local memory. I then investigate entanglement complexity in terms of how compressible a representation of a given state is. I propose a novel kind of geometric entanglement in terms of matrix-product state representations of fixed bond dimension. This representation is more efficient than storing the full state, and so gives an indication of how much information is needed to reconstruct it. By analysing ground state phase diagrams and the ergodic-to-MBL transition, I find that this quantity is exceedingly effective when employed to detect phase boundaries, even in systems where the phases are not known a priori. Finally, I investigate systems which are informed by the capabilities of currentgeneration experimental devices. I first consider whether MBL is accessible in quantum dot arrays by investigating the properties of the von Neumann entropy, imbalance, and number entropy. I then consider phase crossovers in twin-rail quantum dot devices using the statistics of singlet-triplet profiles and the fidelity susceptibility. Finally, I consider idle information loss in an interacting transmon array which simulates IBM’s quantum computers.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Informational Aspects of Quantum Many-Body Systems |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2023. 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-pp.ucl.ac.uk/id/eprint/10178545 |
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