Universität zu Köln

Alcalde Puente, Daniel ORCID: 0000-0002-3519-5931 (2025). Measurement-Based Quantum State Preparation and Ground State Search. PhD thesis, Universität zu Köln.

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Abstract

This thesis introduces and systematically analyzes novel measurement-based quantum state preparation protocols in one dimension, leveraging non-unitary dynamics, quantum measurements, and adaptive feedback mechanisms. Additionally, a stochastic sampling-based approach for ground state search using Projected Entangled Pair States (PEPS) in two dimensions is investigated, further expanding the computational toolkit for simulating complex quantum states. A central contribution is the development of a protocol that employs periodic measurement and resetting of ancilla systems, explicitly applied to the preparation of the one-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) state. We identify an optimal reset interval, balancing entanglement generation and convergence speed, and demonstrate robustness against realistic experimental noise such as dephasing. Furthermore, this thesis introduces a self-learning adaptive measurement-feedback framework within variational quantum circuits (VQCs). The proposed framework autonomously discovers efficient, constant-depth strategies for deterministic preparation of specific AKLT edge states, outperforming existing analytical protocols. This analysis uncovers and mitigates previously unknown optimization challenges unique to measurement-feedback-based variational quantum circuits. The thesis also advances two-dimensional ground state search by investigating a sampling-based optimization approach for finite PEPS. It demonstrates that PEPS representing physically realistic states are computationally tractable within this sampling framework, in contrast to random states, whose complexity makes them prohibitively difficult to contract. To quantitatively distinguish between computationally easy and hard-to-contract states, a novel diagnostic measure is introduced. The developed methodology is successfully applied to physically significant states, including chiral spin liquids and Rydberg atom arrays with long-range interactions, highlighting its effectiveness in simulating complex states relevant to state-of-the-art cold atom experiments. Overall, the thesis provides methodological and conceptual insights into measurement-based quantum state preparation, optimization landscapes, and tensor network simulations.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Alcalde Puente, Daniel d.alcalde.puente@gmail.com orcid.org/0000-0002-3519-5931 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-789975
Date:	2025
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Measurement UNSPECIFIED Quantum UNSPECIFIED Learning UNSPECIFIED
Date of oral exam:	22 August 2025
Referee:	Name Academic Title Rizzi, Matteo Prof. Dr. Gross, David Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/78997