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Efficient estimation and verification of quantum many-body systems

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Erstveröffentlichung
2019-10-17
DOI
10.18725/OPARU-20627
Dissertation


Authors
Holzäpfel, Milan
Referee
Plenio, Martin B.
Ankerhold, Joachim
Faculties
Fakultät für Naturwissenschaften
Institutions
Institut für Theoretische Physik
Institut für Komplexe Quantensysteme
License
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https://oparu.uni-ulm.de/xmlui/license_opod_v1
Abstract
Quantum systems and tensors share the property that the complexity of their description grows exponentially with the number of physical subsystems or tensor indices. This thesis discusses efficient methods for tensor reconstruction, quantum state estimation and verification, as well as quantum state and process tomography. The methods proposed here can be efficient in the sense that the resource requirements scale only polynomially instead of exponentially with the number of physical subsystems or tensor indices. In numerical and analytical calculations, matrix product state (MPS)/tensor train (TT), projected entangled pair state (PEPS), and hierarchical Tucker representations are used. The reconstruction and estimation methods are discussed in principle, their performance is evaluated with numerical simulations, and the quantum state in an ion trap quantum simulator experiment is estimated and verified.
Date created
2019
Funding information
Alexander von Humboldt-Stiftung / Alexander von Humboldt-Professur
US Army Research Office [W91-1NF-14-1-0133]
QuOReP, Quanten-Repeater-Plattform mit Methoden der Quantenoptik / BMBF
HPC-Cluster Theoretische Chemie / DFG [236232410, INST 40/467-1 FUGG]
Quantum-enabled Enhancements in presence of Noise (QueEN) / EPSRC [EP/K04057X/1]
EU Project
BIOQ / Diamond Quantum Devices and Biology / EC / FP7 / 319130
EQUAM / Emulators of Quantum Frustrated Magnetism / EC / FP7 / 323714
QUCHIP / Quantum Simulation on a Photonic Chip / EC / H2020 / 641039
SIQS / Simulators and Interfaces with Quantum Systems / EC / FP7 / 600645
Subject Headings
Quantenzustand [GND]
Spannungstensor [GND]
Maximum-Likelihood-Schätzung [GND]
Schwellenwert [GND]
Tensor fields [LCSH]
Quantum theory-Mathematics [LCSH]
Mathematical physics [LCSH]
Keywords
Quantum state estimation; Quantum state tomography; Quantum process tomography; Ancilla-assisted process tomography; Quantum time evolution; Matrix product state; Matrix product operator; Tensor train; Projected entangled pair state; Tucker representation; Tensor reconstruction; Lieb-Robinson bound; Maximum likelihood estimation; Singular value thresholding
Dewey Decimal Group
DDC 500 / Natural sciences & mathematics
DDC 530 / Physics

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Citation example

Holzäpfel, Milan (2019): Efficient estimation and verification of quantum many-body systems. Open Access Repositorium der Universität Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-20627

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