Thesis
Deterministic fast scramblers
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2023
- Thesis identifier
- T16493
- Person Identifier (Local)
- 201880101
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- Fast scramblers are quantum systems which spread many-body entanglement in a timescale which only grows logarithmically with the system size N. As originated in the theoretical investigations of the non-equilibrium properties of black holes, it is conjectured that they set O(logN) bound on how fast a physical system can scramble information. In this thesis, we propose and investigate two deterministic fast scramblers—a Hamiltonian quantum spin system and a Floquet (iterative) quantum circuit. The models we investigate are on a sparsely coupled graph, where two sites are connected if they are separated by an integer power of 2. We show that these models interpolate between nearest-neighbor spin systems in linear (Euclidean) and treelike (2-adic) geometries. The fast scrambling dynamics, then, emerges as a result of the loss of locality in the models near the point where the underlying geometry transitions. Furthermore, we investigate how deterministic and fast scrambling dynamics influence the systems’ robustness to entanglement destroying operations by performing random projective measurements to the Floquet scrambler. We investigate the critical properties of the measurement-induced phase transitions and dynamically generated quantum error-correcting codes of the model. In both analyses, we found that the fast scrambling dynamics plays a role in protecting the entanglement. The models we propose can be implemented in the near-term experiments. The Hamiltonian fast scrambler can be implemented with cold atoms in an optical cavity by utilizing the Zeeman shift induced by an external magnetic field. The Floquet fast scrambler can be implemented with cold atoms with optical tweezer array, where a complex geometry is created by systematically changing neighboring atoms through shuffling operations. These models provide rich playgrounds for investigating fast scrambling dynamics and corresponding phenomena in the contexts of both theory and experiment.
- Advisor / supervisor
- Daley, Andrew J.
- Resource Type
- DOI
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PDF of thesis T16493 | 2023-03-07 | Pubblico | Scaricare |