Farshi, Thomas;
(2022)
Mixing and localisation in time-periodic quantum circuits.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
This thesis introduces and analyses a new model of time-periodic (Floquet) dynamics in a quantum spin systems. This model is implemented via a time-periodic quantum circuit with local Clifford gates. All the results of this thesis are rigorous mathematical proofs, which use tools and methods from quantum information science to study problems in many-body quantum systems and condensed-matter physics. This includes proofs of a form of dynamical mixing of Pauli operators in the case of local interactions, and conditions under which the evolution operator can resemble a random unitary. The scrambling time is of critical importance to these results, and in the case of non-local interactions, a slightly larger than logarithmic scrambling time is found. Also, the model analysed in this thesis has the peculiarity that it displays a strong form of localisation in one spatial dimension and the absence of localisation in two dimensions. There is no previously known model with these features, hence, this research is important to characterise the landscape of many-body quantum physics.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Mixing and localisation in time-periodic quantum circuits |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. 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 > 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 UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10155519 |
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