DIMACS REU 2026 · Bar-Ilan University
This project studies how quantum measurements, feedback, stochasticity, unitary dynamics, and noise can reshape phases of matter in the Affleck-Kennedy-Lieb-Tasaki (AKLT) model.
Project overview
In ordinary closed quantum systems, unitary dynamics preserves information. Measurements do something different: they extract information, disturb the state, and can compete with entangling dynamics. When this competition is tuned, a many-body system may cross between qualitatively different regimes of entanglement and order.
The AKLT model provides a structured setting for studying this question because it has a well-understood ground-state structure and a natural connection to quantum spin chains, matrix-product-state intuition, and symmetry-protected topological order.
This page is intentionally high-level. It does not include unpublished numerical data, detailed code output, proofs, or internal computations.
Research direction
Start from the known structure of the AKLT model and reconstruct the relevant baseline behavior used by the group.
Replace an adiabatic-measurement protocol with a feedback-based measurement protocol and compare the resulting qualitative behavior.
Turn deterministic feedback choices into stochastic measurement trajectories, then study the ensemble-level behavior.
Add coherent time evolution and depolarizing noise, then ask whether the observed phase transitions persist, shift, or change character.
Research journal
The journal below is a public-facing research log: it records goals, ideas, and conceptual progress without exposing unpublished calculations or detailed results.
I focused on becoming familiar with the AKLT model, the relevant language of measurement-induced phase transitions, and the basic physical questions behind the project. The main goal was to understand the model well enough to reproduce and modify existing protocols responsibly.
I worked on reproducing the group's previous results and began replacing their adiabatic measurement procedure with a feedback-based measurement protocol. This week was centered on checking that the modified protocol was implemented consistently before drawing any conclusions from it.
I generalized the feedback measurements into stochastic measurement trajectories. The focus shifted from a single controlled rule to an ensemble of possible measurement histories, which is closer to the kind of randomness expected in monitored quantum systems.
I added unitary dynamics to the measurement protocol and started testing whether the phase transitions observed in the measurement-only setting also appear when coherent time evolution is present. The central question is whether unitary dynamics preserves, shifts, smooths, or qualitatively changes the transition behavior.
I replaced the previous correction rule with a repair mechanism based on spin ladder operators. This provided a more direct, physically motivated way to move undesired local spin outcomes toward the target sector.
I incorporated coherent unitary evolution into the ladder-operator repair protocol and began studying how the added dynamics competes with the measurement-and-repair process.
I introduced depolarizing noise into the updated protocol to test how robust its qualitative behavior is when the system is exposed to generic local noise.
The final week is devoted to organizing the project into a clear written account, consolidating the physical motivation, methods, and main conclusions developed throughout the program.
Contact
I am Oz Arie, a physics student at Bar-Ilan University participating in the DIMACS REU program. My current research interests include quantum many-body dynamics, monitored quantum systems, tensor-network intuition, and measurement-induced phases.